Mercurial > repos > public > sbplib
comparison +rv/+time/rungekuttaRV.m @ 1033:037f203b9bf5 feature/burgers1d
Merge with branch feature/advectioRV to utilize the +rv package
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Thu, 17 Jan 2019 10:44:12 +0100 |
| parents | 2d7c1333bd6c |
| children | 010bb2677230 |
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| 854:18162a0a5bb5 | 1033:037f203b9bf5 |
|---|---|
| 1 % Takes one time step of size dt using the rungekutta method | |
| 2 % starting from v and where the function F(v,t,RV) gives the | |
| 3 % time derivatives. coeffs is a struct holding the RK coefficients | |
| 4 % for the specific method. RV is the residual viscosity which is updated | |
| 5 % in between the stages and after the updated solution is computed. | |
| 6 function v = rungekuttaRV(v, t , dt, F, RV, DvDt, coeffs) | |
| 7 % Move one stage outside to avoid branching for updating the | |
| 8 % residual inside the loop. | |
| 9 k = zeros(length(v), coeffs.s); | |
| 10 k(:,1) = F(v,t,RV.evaluate(v,DvDt(v))); | |
| 11 | |
| 12 % Compute the intermediate stages k | |
| 13 for i = 2:coeffs.s | |
| 14 u = v; | |
| 15 for j = 1:i-1 | |
| 16 u = u + dt*coeffs.a(i,j)*k(:,j); | |
| 17 end | |
| 18 %RV.update(0.5*(u+v),(u-v)/(coeffs.c(i)*dt)); % Crank-Nicholson for time discretization | |
| 19 k(:,i) = F(u,t+coeffs.c(i)*dt, RV.evaluate(u,DvDt(u))); | |
| 20 end | |
| 21 | |
| 22 % Compute the updated solution as a linear combination | |
| 23 % of the intermediate stages. | |
| 24 u = v; | |
| 25 for i = 1:coeffs.s | |
| 26 u = u + dt*coeffs.b(i)*k(:,i); | |
| 27 end | |
| 28 %RV.update(0.5*(u+v),(u-v)/dt); % Crank-Nicholson for time discretization | |
| 29 v = u; | |
| 30 end |