[전산열유체역학(CFD)] Inviscid Burgers equation에 FVM적용하기

소개

"[전산열유체역학(CFD)] Inviscid Burgers equation에 FVM적용하기"에 대한 내용입니다.

목차

1. First order upwind scheme
1 ) Code
2 ) Graph

2. second order scheme without limiter
1) Code
2) Graph

3. 2nd order scheme with limiter superbee
1) Code
2) Graph

4. 2nd order scheme with limiter van Leer
1) Code
2) Graph

5. 2nd order scheme with limiter minmod
1) Code
2) Graph

6. Compare each FVM method in one graph
1) Code
2) Graph

본문내용

이번 과제는 Non-linear 한 Inviscid Burgers equation에 대하여 first order upwind, second order scheme without limiter, and 2nd order scheme with limiters such as superbee, van Leer,and minmod method를 적용하여 충격파의 시간에 따른 위치를 확인하는 과제입니다.

1. First order upwind scheme
1 ) Code
% first-order upwind method
clc,clear

% step size : c = 1
dx = 0.1;
dt = 0.1;

x = 0:0.1:4;
% initial condition

u = zeros(19,41);
u(1,1:21) = 1;
% boundary condition
u(:,1) = 1;

for n = 1:18
for i = 2:40
u(n+1,i) = u(n,i) - (dt/(2*dx))*(u(n,i)^2 - u(n,i-1)^2);
end
end

fig1 = figure(1);
plot(x,u(1,:),'-d',x,u(7,:),'-^',x,u(13,:),'-v',x,u(19,:),'->')
set(fig1,'OuterPosition',[3 3 600 500])
title({'Solution of the inviscid Burgers equation','by the first-order upwind scheme, delta x = 0.1 and delta t = 0.1'},'FontSize',12)
xlabel('x'), ylabel('u')
legend('t = 0.0 sec','t = 0.6 sec','t = 1.2 sec','t = 1.8 sec')
axis([0 4 -0.2 1.6])

참고자료

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