Mercurial > repos > public > sbplib

annotate +rv/+time/rungekuttaRV.m @ 1019:f029b97dbc72 feature/advectionRV

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Support upwind opSet in Utux2d
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 14 Dec 2018 18:30:27 +0100
parents 2d7c1333bd6c
children 010bb2677230
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
1 % Takes one time step of size dt using the rungekutta method
1012
1e437c9e5132 Create residual viscosity package +rv and generalize the ResidualViscosity class
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 847
diff changeset
2 % starting from v and where the function F(v,t,RV) gives the
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
3 % time derivatives. coeffs is a struct holding the RK coefficients
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
4 % for the specific method. RV is the residual viscosity which is updated
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
5 % in between the stages and after the updated solution is computed.
1017
2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
diff changeset
6 function v = rungekuttaRV(v, t , dt, F, RV, DvDt, coeffs)
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
7 % Move one stage outside to avoid branching for updating the
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
8 % residual inside the loop.
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
9 k = zeros(length(v), coeffs.s);
1017
2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
diff changeset
10 k(:,1) = F(v,t,RV.evaluate(v,DvDt(v)));
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
11
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
12 % Compute the intermediate stages k
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
13 for i = 2:coeffs.s
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
14 u = v;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
15 for j = 1:i-1
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
16 u = u + dt*coeffs.a(i,j)*k(:,j);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
17 end
1017
2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
diff changeset
18 %RV.update(0.5*(u+v),(u-v)/(coeffs.c(i)*dt)); % Crank-Nicholson for time discretization
2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
diff changeset
19 k(:,i) = F(u,t+coeffs.c(i)*dt, RV.evaluate(u,DvDt(u)));
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
20 end
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
21
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
22 % Compute the updated solution as a linear combination
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
23 % of the intermediate stages.
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
24 u = v;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
25 for i = 1:coeffs.s
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
26 u = u + dt*coeffs.b(i)*k(:,i);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
27 end
1017
2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
diff changeset
28 %RV.update(0.5*(u+v),(u-v)/dt); % Crank-Nicholson for time discretization
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
29 v = u;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
30 end