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- P[x_, y_, t_] = e[x, y, t]/([Gamma] - 1) ;
- e[x_, y_, t_] = ([Gamma] - 1) [Rho][x, y, t]/([Mu] mu )
- kb T[x, y, t];
- cp = 5/2 kb/([Mu] mu);
- Rgas = 8.3144598;
- cv = 5/2 kb/([Mu] mu) - Rgas;
- [Gamma] = cp/cv;
- g = 28.02*9.81;
- [Mu] = 0.6163328197226503`;
- mu = 1.66053904*10^-27;
- kb = 1.38064852*10^-23;
- sol1 = NDSolve[{
- D[[Rho][x, y, t]*u[x, y, t],
- t] == -D[[Rho][x, y, t]*u[x, y, t]*u[x, y, t] + P[x, y, t], x] -
- D[[Rho][x, y, t]*u[x, y, t]*v[x, y, t], y],
- D[[Rho][x, y, t]*v[x, y, t],
- t] == -D[[Rho][x, y, t]*v[x, y, t]*u[x, y, t], y] -
- D[[Rho][x, y, t]*v[x, y, t]*v[x, y, t] + P[x, y, t], y] +
- g [Rho][x, y, t],
- D[[Rho][x, y, t], t] == -D[[Rho][x, y, t]*u[x, y, t], x] -
- D[[Rho][x, y, t]*v[x, y, t], y],
- D[e[x, y, t], t] == -D[u[x, y, t]*e[x, y, t], x] -
- D[v[x, y, t]*e[x, y, t], y] -
- P[x, y, t]*(D[u[x, y, t], x] - D[v[x, y, t], y]),
- v[0, y, t] == v[12*10^6, y, t],
- u[0, y, t] == u[12*10^6, y, t],
- T[0, y, t] == T[12*10^6, y, t],
- [Rho][0, y, t] == [Rho][12*10^6, y, t],
- e[0, y, t] == e[12*10^6, y, t],
- (D[u[x, y, t], x] /. x -> 0) == (D[u[x, y, t], x] /. x -> 12000000),
- (D[v[x, y, t], x] /. x -> 0) == (D[v[x, y, t], x] /. x -> 12000000),
- D[u[0, y, t], y] == D[u[12000000, y, t], y],
- D[v[0, y, t], y] == D[v[12000000, y, t], y],
- D[u[0, y, t], t] == D[u[12000000, y, t], t],
- D[v[0, y, t], t] == D[v[12000000, y, t], t],
- (D[T[x, y, t], x] /. x -> 0) == (D[T[x, y, t], x] /. x -> 12000000),
- (D[[Rho][x, y, t], x] /. x -> 0) == (D[[Rho][x, y, t], x] /.
- x -> 12000000),
- D[T[0, y, t], y] == D[T[12000000, y, t], y],
- D[[Rho][0, y, t], y] == D[[Rho][12000000, y, t], y],
- D[T[0, y, t], t] == D[T[12000000, y, t], t],
- D[[Rho][0, y, t], t] == D[[Rho][12000000, y, t], t],
- P[x, 0, t] == 3.83767261162/([Gamma] - 1),
- v[x, 4000000, t] == 0,
- v[x, 0, t] == 0,
- (D[u[x, y, t], y] /. y -> 0) == 0,
- (D[u[x, y, t], y] /. y -> 4000000) == 0,
- v[x, y, 0] == 0,
- u[x, y, 0] == 0,
- T[x, y, 0] == 5770 + 0.00835414960707927 y*10^6,
- [Rho][x, y, 0] ==
- 1.42*10^-7*1.408*10^3 + 7.3561137493644*10^-10 y*10^6
- },
- {u, v, T, [Rho]}, {x, 0, 12000000}, {y, 0, 4000000}, {t, 0, 100},
- StartingStepSize -> {40000, 40000, 1}]
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