Mercurial > repos > public > sbplib
diff +rv/+time/rungekuttaRV.m @ 1012:1e437c9e5132 feature/advectionRV
Create residual viscosity package +rv and generalize the ResidualViscosity class
- Generalize residual viscosity, by passing user-defined flux and calculating the time derivative outside of the update.
- Create separate RungekuttaRV specifically using interior RV updates
- Separate the artifical dissipation operator from the scheme AdvectionRV1D so that the same scheme can be reused for creating the diff op used by the ResidualViscosity class
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Wed, 05 Dec 2018 13:44:10 +0100 |
| parents | +time/+rk/rungekuttaRV.m@1c6f1595bb94 |
| children | 2d7c1333bd6c |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+rv/+time/rungekuttaRV.m Wed Dec 05 13:44:10 2018 +0100 @@ -0,0 +1,30 @@ +% Takes one time step of size dt using the rungekutta method +% starting from v and where the function F(v,t,RV) gives the +% time derivatives. coeffs is a struct holding the RK coefficients +% for the specific method. RV is the residual viscosity which is updated +% in between the stages and after the updated solution is computed. +function v = rungekuttaRV(v, t , dt, F, RV, coeffs) + % Move one stage outside to avoid branching for updating the + % residual inside the loop. + k = zeros(length(v), coeffs.s); + k(:,1) = F(v,t,RV.getViscosity()); + + % Compute the intermediate stages k + for i = 2:coeffs.s + u = v; + for j = 1:i-1 + u = u + dt*coeffs.a(i,j)*k(:,j); + end + RV.update(0.5*(u+v),(u-v)/(coeffs.c(i)*dt)); % Crank-Nicholson for time discretization + k(:,i) = F(u,t+coeffs.c(i)*dt, RV.getViscosity()); + end + + % Compute the updated solution as a linear combination + % of the intermediate stages. + u = v; + for i = 1:coeffs.s + u = u + dt*coeffs.b(i)*k(:,i); + end + RV.update(0.5*(u+v),(u-v)/dt); % Crank-Nicholson for time discretization + v = u; +end