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annotate +rv/+time/rungekuttaRV.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents 2d7c1333bd6c
children 010bb2677230
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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
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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:
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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:
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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:
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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
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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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
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19 k(:,i) = F(u,t+coeffs.c(i)*dt, RV.evaluate(u,DvDt(u)));
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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:
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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:
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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:
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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:
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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:
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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:
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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