Changes between Version 38 and Version 39 of u/erica/MusclHancock
 Timestamp:
 06/18/13 13:26:30 (11 years ago)
Legend:
 Unmodified
 Added
 Removed
 Modified

u/erica/MusclHancock
v38 v39 28 28 where u is the vector of conserved variables (u=u(x,t)), and f is the flux function. Adhering to the IVBP known as the Riemann Problem (i.e. constant left and right data states separated by an initial discontinuity), we solve this system of equations using the fully discrete, explicit, conservative formula: 29 29 30 [[latex($ u_i^ {n+1} = u_i ^n + \frac{\triangle t}{\triangle x}[f_{i1/2}  f_{i+1/2}] *$)]]30 [[latex($ u_i^ {n+1} = u_i ^n + \frac{\triangle t}{\triangle x}[f_{i1/2}  f_{i+1/2}] (*)$)]] 31 31 32 32 for each element of u, where f is the numerical flux. For the 1st order Godunov scheme studied previously, f was taken to simply be the physical flux of 2 adjacent cells, evaluated using the solution to the Local Riemann Problem at the intercell boundary. We have seen various approximation methods to this Godonov scheme, some which estimate the solution of the Riemann problem itself along these intercell boundaries, and others that instead approximate the numerical flux at these boundaries. Next, we will see how the MH scheme produces a 2ndorder accurate solution to the problem. The MH scheme proceeds as follows, being broken down into 3 distinct steps. … … 105 105 = Results = 106 106 107 As you can see here, the MH scheme + Superbee slope limiter + Roe solver produce highly nondiffusive results. However, there still are some small scale spurious oscillations near the boundary of the square wave. 108 107 109 [[Image(MusclRho.png, 35%)]], [[Image(ToroMusclRho.png, 20%)]] 108 110