# couette_BB.rar

• pearson96
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• matlab
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• 2019-10-17 20:41
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couette_BB.rar
• couette_BB.m
3.6KB

% This code accompanies % The Lattice Boltzmann Method: Principles and Practice % T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, E.M. Viggen % ISBN 978-3-319-44649-3 (Electronic) % 978-3-319-44647-9 (Print) % http://www.springer.com/978-3-319-44647-9 % % This code is provided under the MIT license. See LICENSE.txt. % % Author: Goncalo Silva % % Example matlab code for computing a Couette flow with BB % Solves problems from Section 5.3.3.6 in book clear all close all clc % simulation parameters scale=1; % set simulation size NX=5*scale; % channel length NY=5*scale; % channel width NSTEPS=1e4*scale^2; % number of simulation time steps tau=0.9; % relaxation time (BGK model) omega=1/tau; u_max=0.1/scale; % maximum velocity nu=(2*tau-1)/6; % kinematic shear viscosity Re=NY*u_max/nu; % Reynolds number; scaling parameter in simulation % Lattice parameters; note zero direction is last NPOP=9; % number of velocities w = [1/9 1/9 1/9 1/9 1/36 1/36 1/36 1/36 4/9]; % weights cx = [1 0 -1 0 1 -1 -1 1 0]; % velocities, x components cy = [0 1 0 -1 1 1 -1 -1 0]; % velocities, y components % Node locations x = (1:NX)-0.5; y = (1:NY)-0.5; % Analytical solution: Couette velocity u_analy=u_max/NY.*y; % initialize populations feq=zeros(NX,NY,NPOP); for k=1:NPOP feq(:,:,k)=w(k); % assuming density equal one and zero velocity initial state end f=feq; fprop=feq; % convergence parameters tol=1e-12; % tolerance to steady state convergence teval=100; % time step to evaluate convergence u_old=zeros(NX,NY); % initalize clock tstart = tic; % Main algorithm for t=1:NSTEPS % Compute macroscopic quantities % density rho = sum(fprop,3); % momentum components u = sum(fprop(:,:,[1 5 8]),3) - sum(fprop(:,:,[3 6 7]),3); v = sum(fprop(:,:,[2 5 6]),3) - sum(fprop(:,:,[4 7 8]),3); % check convergence if mod(t,teval)==1 conv = abs(mean(u(:))/mean(u_old(:))-1); if conv<tol break else u_old = u; end end for k=1:NPOP % Compute equilibrium distribution (linear equilibrium with incompressible model) feq(:,:,k)=w(k)*(rho + 3*(u*cx(k)+v*cy(k))); end % Collision step f = (1-omega)*fprop + omega*feq; for k=1:NPOP for j=1:NY for i=1:NX % Streaming step (Periodic streaming of whole domain) newx=1+mod(i-1+cx(k)+NX,NX); newy=1+mod(j-1+cy(k)+NY,NY); fprop(newx,newy,k)=f(i,j,k); end end end % Boundary condition (bounce-back) % Top wall (moving with tangential velocity u_max) fprop(:,NY,4)=f(:,NY,2); fprop(:,NY,7)=f(:,NY,5)-(1/6)*u_max; fprop(:,NY,8)=f(:,NY,6)+(1/6)*u_max; % Bottom wall (rest) fprop(:,1,2)=f(:,1,4); fprop(:,1,5)=f(:,1,7); fprop(:,1,6)=f(:,1,8); % % % VISUALIZATION % if (mod(NSTEPS,5)==0) % s = reshape(sqrt(u.^2+v.^2),NX,NY); % imagesc(s'); % axis equal off; drawnow % end end % Calculate performance information after the simulation is finished runtime = toc(tstart); % Compute error: L2 norm error=zeros(NX,1); for i=1:NX error(i)=(sqrt(sum((u(i,:)-u_analy).^2)))./sqrt(sum(u_analy.^2)); end L2=1/NX*sum(error); % Accuracy information fprintf(' ----- accuracy information -----\n'); fprintf(' L2(u): %g\n',L2);

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