Commit 6e7c0ebd by Lambert Theisen 🚀

### Add div(u) term to energy equation (heat)

```- density formulation has no prob
- but pressure formulation is then non (anti-)symmetric
- therefore use mass balance to eliminate div(u)=f_mass from LHS of energy equation to remain (a-)sym
- This needs the removal of unneeded mass source from heat testcases
- Also needs adapting R13 cases such that for mass source, the same energy source is applied s.t. energy equation remains equal
- The latter is actually only needed to compare with WK19 where div(u) was inconsistently neglected```
parent 16c01e27
 ... ... @@ -641,7 +641,8 @@ class Solver: n(r) * bcs[bc]["theta_w"] * df.ds(bc) for bc in bcs.keys() ]) rhs[1] = f_heat * kappa * df.dx # Use div(u)=f_mass to remain sym. (density-form doesnt need this): rhs[1] = (f_heat-f_mass) * kappa * df.dx rhs[2] = - sum([ nt(psi) * bcs[bc]["u_t_w"] * df.ds(bc) + ( ... ...
 ... ... @@ -65,7 +65,7 @@ mode: heat kn: 0.1 xi_tilde: 1.0 heat_source: 2.0 - 1.0 * pow(sqrt(pow(x[0],2)+pow(x[1],2)),2) mass_source: 2.0/5.0 * (1.0 - (5.0*std::pow(sqrt(pow(x[0],2)+pow(x[1],2)),2))/(18.0*pow(kn,2))) * std::cos(phi) mass_source: 0 body_force: [0,0] # Boundary Conditions ... ...
 ... ... @@ -65,7 +65,7 @@ mode: heat kn: 0.1 xi_tilde: 1.0 heat_source: 2.0 - 1.0 * pow(sqrt(pow(x[0],2)+pow(x[1],2)),2) mass_source: 2.0/5.0 * (1.0 - (5.0*std::pow(sqrt(pow(x[0],2)+pow(x[1],2)),2))/(18.0*pow(kn,2))) * std::cos(phi) mass_source: 0 body_force: [0,0] # Boundary Conditions ... ...
 ... ... @@ -65,7 +65,7 @@ mode: heat kn: 0.1 xi_tilde: 1.0 heat_source: 2.0 - 1.0 * pow(sqrt(pow(x[0],2)+pow(x[1],2)),2) mass_source: 2.0/5.0 * (1.0 - (5.0*std::pow(sqrt(pow(x[0],2)+pow(x[1],2)),2))/(18.0*pow(kn,2))) * std::cos(phi) mass_source: 0 body_force: [0,0] # Boundary Conditions ... ...
 ... ... @@ -66,7 +66,7 @@ mode: heat kn: 10.0 xi_tilde: 1.0 heat_source: 2.0 - 1.0 * pow(sqrt(pow(x[0],2)+pow(x[1],2)),2) mass_source: 2.0/5.0 * (1.0 - (5.0*std::pow(sqrt(pow(x[0],2)+pow(x[1],2)),2))/(18.0*pow(kn,2))) * std::cos(phi) mass_source: 0 body_force: [0,0] # Boundary Conditions ... ...
 ... ... @@ -64,7 +64,7 @@ nsd: 2 mode: r13 kn: 1.0 xi_tilde: 1.0 heat_source: 0 heat_source: 1.0 * (1.0 - (5.0*pow(R,2))/(18.0*pow(kn,2))) * cos(phi) mass_source: 1.0 * (1.0 - (5.0*pow(R,2))/(18.0*pow(kn,2))) * cos(phi) body_force: [0,0] ... ...
 ... ... @@ -62,7 +62,7 @@ nsd: 2 mode: r13 kn: 1.0 xi_tilde: 1.0 heat_source: 0 heat_source: 1.0 * (1.0 - (5.0*pow(R,2))/(18.0*pow(kn,2))) * cos(phi) mass_source: 1.0 * (1.0 - (5.0*pow(R,2))/(18.0*pow(kn,2))) * cos(phi) body_force: [0,0] ... ...
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