{ "cells": [ { "cell_type": "markdown", "id": "20be7199", "metadata": { "editable": true }, "source": [ "\n", "\n", "# Demo - Lid driven cavity\n", "**Mikael Mortensen** (email: `mikaem@math.uio.no`), Department of Mathematics, University of Oslo.\n", "\n", "Date: **May 6, 2019**\n", "\n", "**Summary.** The lid driven cavity is a classical benchmark for Navier Stokes solvers.\n", "This is a demonstration of how the Python module [shenfun](https://github.com/spectralDNS/shenfun) can be used to solve the lid\n", "driven cavity problem with full spectral accuracy using a mixed (coupled) basis\n", "in a 2D tensor product domain. The demo also shows how to use mixed\n", "tensor product spaces for vector valued equations. Note that the regular\n", "lid driven cavity, where the top wall has constant velocity and the\n", "remaining three walls are stationary, has a singularity at the two\n", "upper corners, where the velocity is discontinuous.\n", "Due to their global nature, spectral methods\n", "are usually not very good at handling problems with discontinuities, and\n", "for this reason we will also look at a regularized lid driven cavity,\n", "where the top lid moves according to $(1-x)^2(1+x)^2$, thus removing\n", "the corner discontinuities.\n", "\n", "\n", "\n", "\n", "\n", "

Figure 1: Velocity vectors for the lid driven cavity at Reynolds number 100.

\n", "" ] }, { "cell_type": "markdown", "id": "ffa812f1", "metadata": { "editable": true }, "source": [ "## Navier Stokes equations\n", "\n", "\n", "The nonlinear steady Navier Stokes equations are given in strong form as" ] }, { "cell_type": "markdown", "id": "853e2f60", "metadata": { "editable": true }, "source": [ "$$\n", "\\begin{align*}\n", "\\nu \\nabla^2 \\boldsymbol{u} - \\nabla p &= \\nabla \\cdot \\boldsymbol{u} \\boldsymbol{u} \\quad \\text{in } \\Omega , \\\\ \n", "\\nabla \\cdot \\boldsymbol{u} &= 0 \\quad \\text{in } \\Omega, \\\\ \n", "\\int_{\\Omega} p dx &= 0, \\\\ \n", "\\boldsymbol{u}(x, y=1) = (1, 0) \\, &\\text{ or }\\, \\boldsymbol{u}(x, y=1) = ((1-x)^2(1+x)^2, 0), \\\\ \n", "\\boldsymbol{u}(x, y=-1) &= (0, 0), \\\\ \n", "\\boldsymbol{u}(x=\\pm 1, y) &= (0, 0),\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "282c8f88", "metadata": { "editable": true }, "source": [ "where $\\boldsymbol{u}, p$ and $\\nu$ are, respectively, the\n", "fluid velocity vector, pressure and kinematic viscosity. The domain\n", "$\\Omega = (-1, 1)^2$ and the nonlinear term $\\boldsymbol{u} \\boldsymbol{u}$ is the\n", "outer product of vector $\\boldsymbol{u}$ with itself. Note that the final\n", "$\\int_{\\Omega} p dx = 0$ is there because there is no Dirichlet boundary\n", "condition on the pressure and the system of equations would otherwise be\n", "ill conditioned.\n", "\n", "We want to solve these steady nonlinear Navier Stokes equations with the Galerkin\n", "method, using the [shenfun](https://github.com/spectralDNS/shenfun) Python\n", "package. The first thing we need to do then is to import all of shenfun's\n", "functionality" ] }, { "cell_type": "code", "execution_count": 1, "id": "ab478fd9", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:10.882069Z", "iopub.status.busy": "2026-06-03T08:50:10.881976Z", "iopub.status.idle": "2026-06-03T08:50:11.418414Z", "shell.execute_reply": "2026-06-03T08:50:11.418167Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "from shenfun import *" ] }, { "cell_type": "markdown", "id": "9ae78d5e", "metadata": { "editable": true }, "source": [ "Note that MPI for Python ([mpi4py](https://bitbucket.org/mpi4py/mpi4py))\n", "is a requirement for shenfun, but the current solver cannot be used with more\n", "than one processor." ] }, { "cell_type": "markdown", "id": "a178b88b", "metadata": { "editable": true }, "source": [ "## Tensor product spaces\n", "\n", "\n", "With the Galerkin method we need function spaces for both velocity and\n", "pressure, as well as for the\n", "nonlinear right hand side. A Dirichlet space will be used for velocity,\n", "whereas there is no boundary restriction on the pressure space. For both\n", "two-dimensional spaces we will use one basis function for the $x$-direction,\n", "$\\mathcal{X}_k(x)$, and one for the $y$-direction, $\\mathcal{Y}_l(y)$. And\n", "then we create two-dimensional basis functions like" ] }, { "cell_type": "markdown", "id": "027c6861", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "v_{kl}(x, y) = \\mathcal{X}_k(x) \\mathcal{Y}_l(y), \\label{eq:nstestfunction} \\tag{1}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "e5e81b40", "metadata": { "editable": true }, "source": [ "and solutions (trial functions) as" ] }, { "cell_type": "markdown", "id": "481b9ff7", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", " u(x, y) = \\sum_{k}\\sum_{l} \\hat{u}_{kl} v_{kl}(x, y). \\label{eq:nstrialfunction} \\tag{2}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "7d65380f", "metadata": { "editable": true }, "source": [ "For the homogeneous Dirichlet boundary condition the basis functions\n", "$\\mathcal{X}_k(x)$ and $\\mathcal{Y}_l(y)$ are chosen as composite\n", "Legendre polynomials (we could also use Chebyshev):" ] }, { "cell_type": "markdown", "id": "182499a2", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "\\mathcal{X}_k(x) = L_k(x) - L_{k+2}(x), \\quad \\forall \\, k \\in \\boldsymbol{k}^{N_0-2}, \\label{eq:D0} \\tag{3} \n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "dbf64c5f", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation} \n", "\\mathcal{Y}_l(y) = L_l(y) - L_{l+2}(y), \\quad \\forall \\, l \\in \\boldsymbol{l}^{N_1-2}, \\label{eq:D1} \\tag{4}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "b5c336dd", "metadata": { "editable": true }, "source": [ "where $\\boldsymbol{k}^{N_0-2} = (0, 1, \\ldots, N_0-3)$, $\\boldsymbol{l}^{N_1-2} = (0, 1, \\ldots, N_1-3)$\n", "and $N = (N_0, N_1)$ is the number\n", "of quadrature points in each direction. Note that $N_0$ and $N_1$ do not need\n", "to be the same. The basis funciton ([3](#eq:D0)) satisfies\n", "the homogeneous Dirichlet boundary conditions at $x=\\pm 1$ and ([4](#eq:D1)) the same\n", "at $y=\\pm 1$. As such, the basis function $v_{kl}(x, y)$ satisfies the homogeneous Dirichlet boundary\n", "condition for the entire domain.\n", "\n", "With shenfun we create these homogeneous spaces, $D_0^{N_0}(x)=\\text{span}\\{L_k-L_{k+2}\\}_{k=0}^{N_0-2}$ and\n", "$D_0^{N_1}(y)=\\text{span}\\{L_l-L_{l+2}\\}_{l=0}^{N_1-2}$ as" ] }, { "cell_type": "code", "execution_count": 2, "id": "f1e8664d", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.420541Z", "iopub.status.busy": "2026-06-03T08:50:11.420274Z", "iopub.status.idle": "2026-06-03T08:50:11.441624Z", "shell.execute_reply": "2026-06-03T08:50:11.441347Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "N = (45, 45)\n", "family = 'Legendre' # or use 'Chebyshev'\n", "quad = 'GL' # for Chebyshev use 'GC' or 'GL'\n", "D0X = FunctionSpace(N[0], family, quad=quad, bc=(0, 0))\n", "D0Y = FunctionSpace(N[1], family, quad=quad, bc=(0, 0))" ] }, { "cell_type": "markdown", "id": "53084c3b", "metadata": { "editable": true }, "source": [ "The spaces are here the same, but we will use `D0X` in the $x$-direction and\n", "`D0Y` in the $y$-direction. But before we use these bases in\n", "tensor product spaces, they remain identical as long as $N_0 = N_1$.\n", "\n", "Special attention is required by the moving lid. To get a solution\n", "with nonzero boundary condition at $y=1$ we need to add one more basis function\n", "that satisfies that solution. In general, a nonzero boundary condition\n", "can be added on both sides of the domain using the following basis" ] }, { "cell_type": "markdown", "id": "68d54031", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "\\mathcal{Y}_l(y) = L_l(y) - L_{l+2}(y), \\quad \\forall \\, l \\in \\boldsymbol{l}^{N_1-2}. \n", "\\label{_auto1} \\tag{5}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "f2e3221a", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation} \n", "\\mathcal{Y}_{N_1-2}(y) = (L_0+L_1)/2 \\quad \\left(=(1+y)/2\\right), \n", "\\label{_auto2} \\tag{6}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "de119ec2", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation} \n", "\\mathcal{Y}_{N_1-1}(y) = (L_0-L_1)/2 \\quad \\left(=(1-y)/2\\right).\n", "\\label{_auto3} \\tag{7}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "7ac8f98b", "metadata": { "editable": true }, "source": [ "And then the unknown component $N_1-2$ decides the value at $y=1$, whereas\n", "the unknown at $N_1-1$ decides the value at $y=-1$. Here we only need to\n", "add the $N_1-2$ component, but for generality this is implemented in shenfun\n", "using both additional basis functions. We create the space\n", "$D_1^{N_1}(y)=\\text{span}\\{\\mathcal{Y}_l(y)\\}_{l=0}^{N_1-1}$ as" ] }, { "cell_type": "code", "execution_count": 3, "id": "496fa575", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.443350Z", "iopub.status.busy": "2026-06-03T08:50:11.443195Z", "iopub.status.idle": "2026-06-03T08:50:11.445379Z", "shell.execute_reply": "2026-06-03T08:50:11.445173Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "D1Y = FunctionSpace(N[1], family, quad=quad, bc=(0, 1))" ] }, { "cell_type": "markdown", "id": "53280b56", "metadata": { "editable": true }, "source": [ "where `bc=(0, 1)` fixes the values for $y=-1$ and $y=1$, respectively.\n", "For a regularized lid driven cavity the velocity of the top lid is\n", "$(1-x)^2(1+x)^2$ and not unity. To implement this boundary condition\n", "instead, we can make use of [sympy](https://www.sympy.org) and\n", "quite straight forward do" ] }, { "cell_type": "code", "execution_count": 4, "id": "522a6cb6", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.446577Z", "iopub.status.busy": "2026-06-03T08:50:11.446504Z", "iopub.status.idle": "2026-06-03T08:50:11.448055Z", "shell.execute_reply": "2026-06-03T08:50:11.447838Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "import sympy\n", "x = sympy.symbols('x')\n", "#D1Y = FunctionSpace(N[1], family, quad=quad, bc=(0, (1-x)**2*(1+x)**2))" ] }, { "cell_type": "markdown", "id": "eeab4c31", "metadata": { "editable": true }, "source": [ "Uncomment the last line to run the regularized boundary conditions.\n", "Otherwise, there is no difference at all between the regular and the\n", "regularized lid driven cavity implementations.\n", "\n", "The pressure basis that comes with no restrictions for the boundary is a\n", "little trickier. The reason for this has to do with\n", "inf-sup stability. The obvious choice of basis functions are the\n", "regular Legendre polynomials $L_k(x)$ in $x$ and $L_l(y)$ in the\n", "$y$-directions. The problem is that for the natural choice of\n", "$(k, l) \\in \\boldsymbol{k}^{N_0} \\times \\boldsymbol{l}^{N_1}$\n", "there are nullspaces and the problem is not well-defined. It turns out\n", "that the proper choice for the pressure basis is simply the regular\n", "Legendre basis functions, but for\n", "$(k, l) \\in \\boldsymbol{k}^{N_0-2} \\times \\boldsymbol{l}^{N_1-2}$.\n", "The bases $P^{N_0}(x)=\\text{span}\\{L_k(x)\\}_{k=0}^{N_0-3}$ and\n", "$P^{N_1}(y)=\\text{span}\\{L_l(y)\\}_{l=0}^{N_1-3}$ are created as" ] }, { "cell_type": "code", "execution_count": 5, "id": "395ae9db", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.449183Z", "iopub.status.busy": "2026-06-03T08:50:11.449114Z", "iopub.status.idle": "2026-06-03T08:50:11.451497Z", "shell.execute_reply": "2026-06-03T08:50:11.451288Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "PX = FunctionSpace(N[0], family, quad=quad)\n", "PY = FunctionSpace(N[1], family, quad=quad)\n", "PX.slice = lambda: slice(0, N[0]-2)\n", "PY.slice = lambda: slice(0, N[1]-2)" ] }, { "cell_type": "markdown", "id": "b046d361", "metadata": { "editable": true }, "source": [ "Note that we still use these spaces with the same $N_0 \\cdot N_1$\n", "quadrature points in real space, but the two highest frequencies have\n", "been set to zero.\n", "\n", "We have now created all relevant function spaces for the problem at hand.\n", "It remains to combine these spaces into tensor product spaces, and to\n", "combine tensor product spaces into mixed (coupled) tensor product\n", "spaces. From the Dirichlet bases we create two different tensor\n", "product spaces, whereas one is enough for the pressure" ] }, { "cell_type": "markdown", "id": "9bd40c28", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "V_{1}^{\\boldsymbol{N}}(\\boldsymbol{x}) = D_0^{N_0}(x) \\otimes D_1^{N_1}(y), \n", "\\label{_auto4} \\tag{8}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "8b9eeee7", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation} \n", "V_{0}^{\\boldsymbol{N}}(\\boldsymbol{x}) = D_0^{N_0}(x) \\otimes D_0^{N_1}(y), \n", "\\label{_auto5} \\tag{9}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "41f3ed7e", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation} \n", "P^{\\boldsymbol{N}}(\\boldsymbol{x}) = P^{N_0}(x) \\otimes P^{N_1}(y).\n", "\\label{_auto6} \\tag{10}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "e27ae020", "metadata": { "editable": true }, "source": [ "With shenfun the tensor product spaces are created as" ] }, { "cell_type": "code", "execution_count": 6, "id": "76747afc", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.452844Z", "iopub.status.busy": "2026-06-03T08:50:11.452779Z", "iopub.status.idle": "2026-06-03T08:50:11.470200Z", "shell.execute_reply": "2026-06-03T08:50:11.469927Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "V1 = TensorProductSpace(comm, (D0X, D1Y))\n", "V0 = TensorProductSpace(comm, (D0X, D0Y))\n", "P = TensorProductSpace(comm, (PX, PY), modify_spaces_inplace=True)" ] }, { "cell_type": "markdown", "id": "2ff12ff2", "metadata": { "editable": true }, "source": [ "where ``modify_spaces_inplace=True`` makes use of ``PX`` and\n", "``PY`` directly. These spaces have now been modified to fit in\n", "the TensorProductSpace ``P``, along two different directions and as such\n", "the original spaces have been modified. The default behavior in shenfun\n", "is to make copies of the 1D spaces under the hood, and thus leave ``PX``\n", "and ``PY`` untouched. In that case the two new and modified spaces would be accessible\n", "from ``P.bases``.\n", "\n", "Note that all these tensor product spaces are scalar valued.\n", "The velocity is a vector, and a vector requires a mixed vector basis like\n", "$W_1^{\\boldsymbol{N}} = V_1^{\\boldsymbol{N}} \\times V_0^{\\boldsymbol{N}}$. The vector basis is created\n", "in shenfun as" ] }, { "cell_type": "code", "execution_count": 7, "id": "9cdaa7ab", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.471503Z", "iopub.status.busy": "2026-06-03T08:50:11.471434Z", "iopub.status.idle": "2026-06-03T08:50:11.473109Z", "shell.execute_reply": "2026-06-03T08:50:11.472868Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "W1 = VectorSpace([V1, V0])\n", "W0 = VectorSpace([V0, V0])" ] }, { "cell_type": "markdown", "id": "d6ac99c7", "metadata": { "editable": true }, "source": [ "Note that the second vector basis, $W_0^{\\boldsymbol{N}} = V_0^{\\boldsymbol{N}} \\times V_0^{\\boldsymbol{N}}$, uses\n", "homogeneous boundary conditions throughout." ] }, { "cell_type": "markdown", "id": "8a6e6122", "metadata": { "editable": true }, "source": [ "## Mixed variational form\n", "\n", "\n", "We now formulate a variational problem using the\n", "Galerkin method: Find\n", "$\\boldsymbol{u} \\in W_1^{\\boldsymbol{N}}$ and $p \\in P^{\\boldsymbol{N}}$ such that" ] }, { "cell_type": "markdown", "id": "9247bcd5", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "\\int_{\\Omega} (\\nu \\nabla^2 \\boldsymbol{u} - \\nabla p ) \\cdot \\boldsymbol{v} \\, dxdy = \\int_{\\Omega} (\\nabla \\cdot \\boldsymbol{u}\\boldsymbol{u}) \\cdot \\boldsymbol{v}\\, dxdy \\quad\\forall \\boldsymbol{v} \\, \\in \\, W_0^{\\boldsymbol{N}}, \\label{eq:nsvarform} \\tag{11} \n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "10e0c889", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation} \n", "\\int_{\\Omega} \\nabla \\cdot \\boldsymbol{u} \\, q \\, dxdy = 0 \\quad\\forall q \\, \\in \\, P^{\\boldsymbol{N}}.\n", "\\label{_auto7} \\tag{12}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "0ecae3eb", "metadata": { "editable": true }, "source": [ "Note that we are using test functions $\\boldsymbol{v}$ with homogeneous\n", "boundary conditions.\n", "\n", "The first obvious issue with Eq ([11](#eq:nsvarform)) is the nonlinearity.\n", "In other words we will\n", "need to linearize and iterate to be able to solve these equations with\n", "the Galerkin method. To this end we will introduce the solution on\n", "iteration $k \\in [0, 1, \\ldots]$ as $\\boldsymbol{u}^k$ and compute the nonlinearity\n", "using only known solutions\n", "$\\int_{\\Omega} (\\nabla \\cdot \\boldsymbol{u}^k\\boldsymbol{u}^k) \\cdot \\boldsymbol{v}\\, dxdy$.\n", "Using further integration by parts we end up with the equations to solve\n", "for iteration number $k+1$ (using $\\boldsymbol{u} = \\boldsymbol{u}^{k+1}$ and $p=p^{k+1}$\n", "for simplicity)" ] }, { "cell_type": "markdown", "id": "6194c91b", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "-\\int_{\\Omega} \\nu \\nabla \\boldsymbol{u} \\, \\colon \\nabla \\boldsymbol{v} \\, dxdy + \\int_{\\Omega} p \\nabla \\cdot \\boldsymbol{v} \\, dxdy = \\int_{\\Omega} (\\nabla \\cdot \\boldsymbol{u}^k\\boldsymbol{u}^k) \\cdot \\boldsymbol{v}\\, dxdy \\quad\\forall \\boldsymbol{v} \\, \\in \\, W_0^{\\boldsymbol{N}}, \\label{eq:nsvarform2} \\tag{13} \n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "9a1bc12e", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation} \n", "\\int_{\\Omega} \\nabla \\cdot \\boldsymbol{u} \\, q \\, dxdy = 0 \\quad\\forall q \\, \\in \\, P^{\\boldsymbol{N}}.\n", "\\label{_auto8} \\tag{14}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "3ad1369a", "metadata": { "editable": true }, "source": [ "Note that the nonlinear term may also be integrated by parts and\n", "evaluated as $\\int_{\\Omega}-\\boldsymbol{u}^k\\boldsymbol{u}^k \\, \\colon \\nabla \\boldsymbol{v} \\, dxdy$. All\n", "boundary integrals disappear since we are using test functions with\n", "homogeneous boundary conditions.\n", "\n", "Since we are to solve for $\\boldsymbol{u}$ and $p$ at the same time, we formulate a\n", "mixed (coupled) problem: find $(\\boldsymbol{u}, p) \\in W_1^{\\boldsymbol{N}} \\times P^{\\boldsymbol{N}}$\n", "such that" ] }, { "cell_type": "markdown", "id": "9d7704be", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "a((\\boldsymbol{u}, p), (\\boldsymbol{v}, q)) = L((\\boldsymbol{v}, q)) \\quad \\forall (\\boldsymbol{v}, q) \\in W_0^{\\boldsymbol{N}} \\times P^{\\boldsymbol{N}},\n", "\\label{_auto9} \\tag{15}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "1004cd02", "metadata": { "editable": true }, "source": [ "where bilinear ($a$) and linear ($L$) forms are given as" ] }, { "cell_type": "markdown", "id": "9bd71ce1", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", " a((\\boldsymbol{u}, p), (\\boldsymbol{v}, q)) = -\\int_{\\Omega} \\nu \\nabla \\boldsymbol{u} \\, \\colon \\nabla \\boldsymbol{v} \\, dxdy + \\int_{\\Omega} p \\nabla \\cdot \\boldsymbol{v} \\, dxdy + \\int_{\\Omega} \\nabla \\cdot \\boldsymbol{u} \\, q \\, dxdy, \n", "\\label{_auto10} \\tag{16}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "068f2a78", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation} \n", " L((\\boldsymbol{v}, q); \\boldsymbol{u}^{k}) = \\int_{\\Omega} (\\nabla \\cdot \\boldsymbol{u}^{k}\\boldsymbol{u}^{k}) \\cdot \\boldsymbol{v}\\, dxdy.\n", "\\label{_auto11} \\tag{17}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "55eeb8fb", "metadata": { "editable": true }, "source": [ "Note that the bilinear form will assemble to a block matrix, whereas the right hand side\n", "linear form will assemble to a block vector. The bilinear form does not change\n", "with the solution and as such it does not need to be reassembled inside\n", "an iteration loop.\n", "\n", "The algorithm used to solve the equations are:\n", "\n", " * Set $k = 0$\n", "\n", " * Guess $\\boldsymbol{u}^0 = (0, 0)$\n", "\n", " * while not converged:\n", "\n", " * assemble $L((\\boldsymbol{v}, q); \\boldsymbol{u}^{k})$\n", "\n", " * solve $a((\\boldsymbol{u}, p), (\\boldsymbol{v}, q)) = L((\\boldsymbol{v}, q); \\boldsymbol{u}^{k})$ for $\\boldsymbol{u}^{k+1}, p^{k+1}$\n", "\n", " * compute error = $\\int_{\\Omega} (\\boldsymbol{u}^{k+1}-\\boldsymbol{u}^{k})^2 \\, dxdy$\n", "\n", " * if error $<$ some tolerance then converged = True\n", "\n", " * $k$ += $1$" ] }, { "cell_type": "markdown", "id": "352eed28", "metadata": { "editable": true }, "source": [ "## Implementation of solver\n", "\n", "We will now implement the coupled variational problem described in previous\n", "sections. First of all, since we want to solve for the velocity and pressure\n", "in a coupled solver, we have to\n", "create a mixed tensor product space $VQ = W_1^{\\boldsymbol{N}} \\times P^{\\boldsymbol{N}}$ that\n", "couples velocity and pressure" ] }, { "cell_type": "code", "execution_count": 8, "id": "53b8bee6", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.474736Z", "iopub.status.busy": "2026-06-03T08:50:11.474667Z", "iopub.status.idle": "2026-06-03T08:50:11.476218Z", "shell.execute_reply": "2026-06-03T08:50:11.475989Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "VQ = CompositeSpace([W1, P]) # Coupling velocity and pressure" ] }, { "cell_type": "markdown", "id": "eb737566", "metadata": { "editable": true }, "source": [ "We can now create test- and trialfunctions for the coupled space $VQ$,\n", "and then split them up into components afterwards:" ] }, { "cell_type": "code", "execution_count": 9, "id": "8aa77ff2", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.477406Z", "iopub.status.busy": "2026-06-03T08:50:11.477333Z", "iopub.status.idle": "2026-06-03T08:50:11.478879Z", "shell.execute_reply": "2026-06-03T08:50:11.478674Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "up = TrialFunction(VQ)\n", "vq = TestFunction(VQ)\n", "u, p = up\n", "v, q = vq" ] }, { "cell_type": "markdown", "id": "980d2ae6", "metadata": { "editable": true }, "source": [ ":::{note}\n", "The test function `v` is using homogeneous Dirichlet boundary conditions even\n", "though it is derived from `VQ`, which contains `W1`. It is currently not (and will\n", "probably never be) possible to use test functions with inhomogeneous\n", "boundary conditions.\n", ":::\n", "\n", "With the basisfunctions in place we may assemble the different blocks of the\n", "final coefficient matrix. For this we also need to specify the kinematic\n", "viscosity, which is given here in terms of the Reynolds number:" ] }, { "cell_type": "code", "execution_count": 10, "id": "31f39748", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.480073Z", "iopub.status.busy": "2026-06-03T08:50:11.479984Z", "iopub.status.idle": "2026-06-03T08:50:11.495004Z", "shell.execute_reply": "2026-06-03T08:50:11.494715Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "Re = 100.\n", "nu = 2./Re\n", "if family.lower() == 'legendre':\n", " A = inner(grad(v), -nu*grad(u))\n", " G = inner(div(v), p)\n", "else:\n", " A = inner(v, nu*div(grad(u)))\n", " G = inner(v, -grad(p))\n", "D = inner(q, div(u))" ] }, { "cell_type": "markdown", "id": "89cba222", "metadata": { "editable": true }, "source": [ "The assembled subsystems `A, G` and `D` are lists containg the different blocks of\n", "the complete, coupled, coefficient matrix. `A` actually contains 4\n", "tensor product matrices of type [TPMatrix](https://shenfun.readthedocs.io/en/latest/shenfun.html#shenfun.matrixbase.TPMatrix). The first two\n", "matrices are for vector component zero of the test function `v[0]` and\n", "trial function `u[0]`, the\n", "matrices 2 and 3 are for components 1. The first two matrices are as such for" ] }, { "cell_type": "markdown", "id": "b2f5defb", "metadata": { "editable": true }, "source": [ " A[0:2] = inner(grad(v[0]), -nu*grad(u[0]))\n" ] }, { "cell_type": "markdown", "id": "62fb6b73", "metadata": { "editable": true }, "source": [ "Breaking it down the inner product is mathematically" ] }, { "cell_type": "markdown", "id": "e8508c5a", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "\\label{eq:partialeq1} \\tag{18}\n", "\\int_{\\Omega}-\\nu \\left(\\frac{\\partial \\boldsymbol{v}[0]}{\\partial x}, \\frac{\\partial \\boldsymbol{v}[0]}{\\partial y}\\right) \\cdot \\left(\\frac{\\partial \\boldsymbol{u}[0]}{\\partial x}, \\frac{\\partial \\boldsymbol{u}[0]}{\\partial y}\\right) dx dy .\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "232abb61", "metadata": { "editable": true }, "source": [ "We can now insert for test function $\\boldsymbol{v}[0]$" ] }, { "cell_type": "markdown", "id": "9eb8662d", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "\\boldsymbol{v}[0]_{kl} = \\mathcal{X}_k \\mathcal{Y}_l, \\quad (k, l) \\in \\boldsymbol{k}^{N_0-2} \\times \\boldsymbol{l}^{N_1-2}\n", "\\label{_auto12} \\tag{19}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "4e50aac5", "metadata": { "editable": true }, "source": [ "and trialfunction" ] }, { "cell_type": "markdown", "id": "ced7ddd5", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", "\\boldsymbol{u}[0]_{mn} = \\sum_{m=0}^{N_0-3} \\sum_{n=0}^{N_1-1} \\hat{\\boldsymbol{u}}[0]_{mn} \\mathcal{X}_m \\mathcal{Y}_n,\n", "\\label{_auto13} \\tag{20}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "4cf2aa34", "metadata": { "editable": true }, "source": [ "where $\\hat{\\boldsymbol{u}}$ are the unknown degrees of freedom for the velocity vector.\n", "Notice that the sum over the second\n", "index runs all the way to $N_1-1$, whereas the other indices runs to either\n", "$N_0-3$ or $N_1-3$. This is because of the additional basis functions required\n", "for the inhomogeneous boundary condition.\n", "\n", "Inserting for these basis functions into ([18](#eq:partialeq1)), we obtain after a few trivial\n", "manipulations" ] }, { "cell_type": "markdown", "id": "ff48c66d", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", " -\\sum_{m=0}^{N_0-3} \\sum_{n=0}^{N_1-1} \\nu \\Big( \\underbrace{\\int_{-1}^{1} \\frac{\\partial \\mathcal{X}_k}{\\partial x} \\frac{\\partial \\mathcal{X}_m}{\\partial x} dx \\int_{-1}^{1} \\mathcal{Y}_l \\mathcal{Y}_n dy}_{A[0]} + \\underbrace{\\int_{-1}^{1} \\mathcal{X}_k X_m dx \\int_{-1}^{1} \\frac{\\partial \\mathcal{Y}_l}{\\partial y} \\frac{\\partial \\mathcal{Y}_n}{\\partial y} dy}_{A[1]} \\Big) \\hat{\\boldsymbol{u}}[0]_{mn}.\n", "\\label{_auto14} \\tag{21}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "e5db0d4c", "metadata": { "editable": true }, "source": [ "We see that each tensor product matrix (both A[0] and A[1]) is composed as\n", "outer products of two smaller matrices, one for each dimension.\n", "The first tensor product matrix, A[0], is" ] }, { "cell_type": "markdown", "id": "57725c54", "metadata": { "editable": true }, "source": [ "\n", "\n", "\n", "$$\n", "\\begin{equation}\n", " \\underbrace{\\int_{-1}^{1} \\frac{\\partial \\mathcal{X}_k}{\\partial x} \\frac{\\partial \\mathcal{X}_m}{\\partial x} dx}_{c_{km}} \\underbrace{\\int_{-1}^{1} \\mathcal{Y}_l \\mathcal{Y}_n dy}_{f_{ln}}\n", "\\label{_auto15} \\tag{22}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "id": "6c7aa78d", "metadata": { "editable": true }, "source": [ "where $C\\in \\mathbb{R}^{N_0-2 \\times N_1-2}$ and $F \\in \\mathbb{R}^{N_0-2 \\times N_1}$.\n", "Note that due to the inhomogeneous boundary conditions this last matrix $F$\n", "is actually not square. However, remember that all contributions from the two highest\n", "degrees of freedom ($\\hat{\\boldsymbol{u}}[0]_{m,N_1-2}$ and $\\hat{\\boldsymbol{u}}[0]_{m,N_1-1}$) are already\n", "known and they can, as such, be moved directly over to the right hand side of the\n", "linear algebra system that is to be solved. More precisely, we can split the\n", "tensor product matrix into two contributions and obtain" ] }, { "cell_type": "markdown", "id": "7a9bb9a5", "metadata": { "editable": true }, "source": [ "$$\n", "\\sum_{m=0}^{N_0-3}\\sum_{n=0}^{N_1-1} c_{km}f_{ln} \\hat{\\boldsymbol{u}}[0]_{m, n} = \\sum_{m=0}^{N_0-3}\\sum_{n=0}^{N_1-3}c_{km}f_{ln}\\hat{\\boldsymbol{u}}[0]_{m, n} + \\sum_{m=0}^{N_0-3}\\sum_{n=N_1-2}^{N_1-1}c_{km}f_{ln}\\hat{\\boldsymbol{u}}[0]_{m, n}, \\quad \\forall (k, l) \\in \\boldsymbol{k}^{N_0-2} \\times \\boldsymbol{l}^{N_1-2},\n", "$$" ] }, { "cell_type": "markdown", "id": "479af7cb", "metadata": { "editable": true }, "source": [ "where the first term on the right hand side is square and the second term is known and\n", "can be moved to the right hand side of the linear algebra equation system.\n", "\n", "At this point all matrices, both regular and boundary matrices, are\n", "contained within the three lists A, G and D. We can now create a solver\n", "for block matrices that incorporates these boundary conditions\n", "automatically" ] }, { "cell_type": "code", "execution_count": 11, "id": "7e7fa5c6", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.497071Z", "iopub.status.busy": "2026-06-03T08:50:11.496967Z", "iopub.status.idle": "2026-06-03T08:50:11.499699Z", "shell.execute_reply": "2026-06-03T08:50:11.499478Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "sol = la.BlockMatrixSolver(A+G+D)" ] }, { "cell_type": "markdown", "id": "8fc81725", "metadata": { "editable": true }, "source": [ "In the solver `sol` there is now a regular block matrix found in\n", "`sol.mat`, which is the symmetric" ] }, { "cell_type": "markdown", "id": "2bdc1587", "metadata": { "editable": true }, "source": [ "$$\n", "\\begin{bmatrix}\n", " A[0]+A[1] & 0 & G[0] \\\\ \n", " 0 & A[2]+A[3] & G[1] \\\\ \n", " D[0] & D[1] & 0\n", " \\end{bmatrix}\n", "$$" ] }, { "cell_type": "markdown", "id": "98bab253", "metadata": { "editable": true }, "source": [ "The boundary matrices are similarly collected in a boundary block matrix\n", "in `sol.bc_mat`. This matrix is used under the hood to modify the\n", "right hand side.\n", "\n", "We now have all the matrices we need in order to solve the Navier Stokes equations.\n", "However, we also need some work arrays for iterations" ] }, { "cell_type": "code", "execution_count": 12, "id": "bd70fd5d", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.500998Z", "iopub.status.busy": "2026-06-03T08:50:11.500912Z", "iopub.status.idle": "2026-06-03T08:50:11.502708Z", "shell.execute_reply": "2026-06-03T08:50:11.502491Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "# Create Function to hold solution. Use set_boundary_dofs to fix the degrees\n", "# of freedom in uh_hat that determines the boundary conditions.\n", "uh_hat = Function(VQ).set_boundary_dofs()\n", "ui_hat = uh_hat[0]\n", "\n", "# New solution (iterative)\n", "uh_new = Function(VQ).set_boundary_dofs()\n", "ui_new = uh_new[0]" ] }, { "cell_type": "markdown", "id": "e6879887", "metadata": { "editable": true }, "source": [ "The nonlinear right hand side also requires some additional attention.\n", "Nonlinear terms are usually computed in physical space before transforming\n", "to spectral. For this we need to evaluate the velocity vector on the\n", "quadrature mesh. We also need a rank 2 Array to hold the outer\n", "product $\\boldsymbol{u}\\boldsymbol{u}$. The required arrays and spaces are\n", "created as" ] }, { "cell_type": "code", "execution_count": 13, "id": "38b7fc85", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.504155Z", "iopub.status.busy": "2026-06-03T08:50:11.504061Z", "iopub.status.idle": "2026-06-03T08:50:11.506052Z", "shell.execute_reply": "2026-06-03T08:50:11.505796Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "bh_hat = Function(VQ)\n", "\n", "# Create arrays to hold velocity vector solution\n", "ui = Array(W1)\n", "\n", "# Create work arrays for nonlinear part\n", "QT = CompositeSpace([W1, W0]) # for uiuj\n", "uiuj = Array(QT)\n", "uiuj_hat = Function(QT)" ] }, { "cell_type": "markdown", "id": "fcb47ed7", "metadata": { "editable": true }, "source": [ "The right hand side $L((\\boldsymbol{v}, q);\\boldsymbol{u}^{k});$ is computed in its\n", "own function `compute_rhs` as" ] }, { "cell_type": "code", "execution_count": 14, "id": "bf45c299", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.507643Z", "iopub.status.busy": "2026-06-03T08:50:11.507535Z", "iopub.status.idle": "2026-06-03T08:50:11.509546Z", "shell.execute_reply": "2026-06-03T08:50:11.509318Z" }, "tags": [ "thebe-init" ] }, "outputs": [], "source": [ "def compute_rhs(ui_hat, bh_hat):\n", " global ui, uiuj, uiuj_hat, V1, bh_hat0\n", " bh_hat.fill(0)\n", " ui = W1.backward(ui_hat, ui)\n", " uiuj = outer(ui, ui, uiuj)\n", " uiuj_hat = uiuj.forward(uiuj_hat)\n", " bi_hat = bh_hat[0]\n", " bi_hat = inner(v, div(uiuj_hat), output_array=bi_hat)\n", " #bi_hat = inner(grad(v), -uiuj_hat, output_array=bi_hat)\n", " return bh_hat" ] }, { "cell_type": "markdown", "id": "880ad1d9", "metadata": { "editable": true }, "source": [ "Here [outer()](https://shenfun.readthedocs.io/en/latest/shenfun.utilities.html#shenfun.utilities.outer) is a shenfun function that computes the\n", "outer product of two vectors and returns the product in a rank two\n", "array (here `uiuj`). With `uiuj` forward transformed to `uiuj_hat`\n", "we can assemble the linear form either as `inner(v, div(uiuj_hat)` or\n", "`inner(grad(v), -uiuj_hat)`.\n", "\n", "Now all that remains is to guess an initial solution and solve\n", "iteratively until convergence. For initial solution we simply set the\n", "velocity and pressure to zero. With an initial solution we are ready\n", "to start iterating.\n", "However, for convergence it is necessary to add some underrelaxation $\\alpha$,\n", "and update the solution each time step as" ] }, { "cell_type": "markdown", "id": "7222104f", "metadata": { "editable": true }, "source": [ "$$\n", "\\begin{align*}\n", "\\hat{\\boldsymbol{u}}^{k+1} &= \\alpha \\hat{\\boldsymbol{u}}^* + (1-\\alpha)\\hat{\\boldsymbol{u}}^{k},\\\\ \n", "\\hat{p}^{k+1} &= \\alpha \\hat{p}^* + (1-\\alpha)\\hat{p}^{k},\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "387876a5", "metadata": { "editable": true }, "source": [ "where $\\hat{\\boldsymbol{u}}^*$ and $\\hat{p}^*$ are the newly computed velocity\n", "and pressure returned from `M.solve`. Without underrelaxation the solution\n", "will quickly blow up. The iteration loop goes as follows" ] }, { "cell_type": "code", "execution_count": 15, "id": "cf3cb47b", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-06-03T08:50:11.511128Z", "iopub.status.busy": "2026-06-03T08:50:11.511029Z", "iopub.status.idle": "2026-06-03T08:50:13.327190Z", "shell.execute_reply": "2026-06-03T08:50:13.326888Z" }, "tags": [ "thebe-init" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration 1 Error 8.5648e+00\n", "Iteration 2 Error 4.2986e+00\n", "Iteration 3 Error 2.1518e+00\n", "Iteration 4 Error 1.0731e+00\n", "Iteration 5 Error 5.3935e-01\n", "Iteration 6 Error 2.7339e-01\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration 7 Error 1.3959e-01\n", "Iteration 8 Error 7.1915e-02\n", "Iteration 9 Error 3.7490e-02\n", "Iteration 10 Error 1.9937e-02\n", "Iteration 11 Error 1.0955e-02\n", "Iteration 12 Error 6.1707e-03\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration 13 Error 3.4384e-03\n", "Iteration 14 Error 1.9036e-03\n", "Iteration 15 Error 1.1460e-03\n", "Iteration 16 Error 7.4978e-04\n", "Iteration 17 Error 4.7012e-04\n", "Iteration 18 Error 2.8977e-04\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration 19 Error 2.0676e-04\n", "Iteration 20 Error 1.5348e-04\n", "Iteration 21 Error 1.0054e-04\n", "Iteration 22 Error 6.2570e-05\n", "Iteration 23 Error 4.4921e-05\n", "Iteration 24 Error 3.3152e-05\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration 25 Error 2.1942e-05\n", "Iteration 26 Error 1.4881e-05\n", "Iteration 27 Error 1.1424e-05\n", "Iteration 28 Error 8.2461e-06\n", "Iteration 29 Error 5.3494e-06\n", "Iteration 30 Error 3.7853e-06\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration 31 Error 2.9557e-06\n", "Iteration 32 Error 2.0822e-06\n", "Iteration 33 Error 1.3564e-06\n", "Iteration 34 Error 9.9917e-07\n", "Iteration 35 Error 7.7367e-07\n", "Iteration 36 Error 5.3417e-07\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration 37 Error 3.5675e-07\n", "Iteration 38 Error 2.6857e-07\n", "Iteration 39 Error 2.0222e-07\n", "Iteration 40 Error 1.3839e-07\n", "Iteration 41 Error 9.6097e-08\n", "Iteration 42 Error 7.2519e-08\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Iteration 43 Error 5.2854e-08\n", "Iteration 44 Error 3.6492e-08\n", "Iteration 45 Error 2.6314e-08\n", "Iteration 46 Error 1.9563e-08\n", "Iteration 47 Error 1.3930e-08\n", "Iteration 48 Error 9.8734e-09\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "converged = False\n", "count = 0\n", "alfa = 0.5\n", "while not converged:\n", " count += 1\n", " bh_hat = compute_rhs(ui_hat, bh_hat)\n", " uh_new = sol(bh_hat, u=uh_new, constraints=((2, 0, 0),))\n", " error = np.linalg.norm(ui_hat-ui_new)\n", " uh_hat[:] = alfa*uh_new + (1-alfa)*uh_hat\n", " converged = abs(error) < 1e-8 or count >= 100\n", " print('Iteration %d Error %2.4e' %(count, error))\n", "\n", "up = uh_hat.backward()\n", "u, p = up\n", "\n", "X = V0.local_mesh(True)\n", "plt.figure()\n", "plt.quiver(X[0], X[1], u[0], u[1])" ] }, { "cell_type": "markdown", "id": "f392e652", "metadata": { "editable": true }, "source": [ "Note that the `constraints=((2, 0, 0),)` keyword argument\n", "ensures that the pressure integrates to zero, i.e., $\\int_{\\Omega} p \\omega dxdy=0$.\n", "Here the number 2 tells us that block component 2 in the mixed space\n", "(the pressure) should be integrated, dof 0 should be fixed, and it\n", "should be fixed to 0.\n", "\n", "The last three lines plots velocity vectors, like also seen in the [figure 1](#fig:drivencavity)\n", "in the top of this demo. The solution is apparently nice\n", "and smooth, but hidden underneath are Gibbs oscillations from the\n", "corner discontinuities. This is painfully obvious when switching from\n", "Legendre to Chebyshev polynomials. With Chebyshev the same plot looks\n", "like the [Figure 2](#fig:drivencavitycheb) below. However, choosing instead the\n", "regularized lid, with no discontinuities, the solutions will be nice and\n", "smooth, both for Legendre and Chebyshev polynomials.\n", "\n", "\n", "\n", "\n", "\n", "

Figure 2: Velocity vectors for Re=100 using Chebyshev.

\n", "" ] }, { "cell_type": "markdown", "id": "b02c599f", "metadata": { "editable": true }, "source": [ "## Complete solver\n", "\n", "\n", "A complete solver can be found in demo [NavierStokesDrivenCavity.py](https://github.com/spectralDNS/shenfun/blob/master/demo/NavierStokesDrivenCavity.py)." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }