Solve the 1D random forced viscous Burgers equation with high order finite element and finite difference methods. Direct Numerical Simulation and Large-Eddy Simulation are possible. The turbulence model implemented for LES is the eddy viscosity Smagorinsky model. Both a constant Smagorinsky model and a dynamic Smagorinsky model are implemented.
The main driver of the code is the file Main.m
The implemented finite element methods are:
- continuous and discontinuous linear Lagrange element
- continuous 3rd order Lagrange element
- continuous and discontinuous 3rd order Hermite element
- continuous 5th order Hermite element
The implemented finite difference schemes are
- energy dissipative 2nd order centered scheme
- energy conservative 2nd order centered scheme
- energy conservative 4th order centered scheme
- energy conservative compact schemes with spectral-like resolution
- non-linear discretization of the convective term (slope-limiters)
The implemented finite difference slope-limiters are chosen from the article "On the spectral and conservation properties of nonlinear discretization operators" by D. Fauconnier and E. Dick. These are the
- central Dynamic Finite Difference (DFD)
- 1st, 2nd and 3rd order upwind discretization (UP1, UP2 and UP3)
- Total Variation Diminishing (TVD) scheme
The non-linear discretization is based on the skew-symmetric form of the convective term.
The energy spectrum is computed and compared with a reference spectrum from a pseudo-spectral code.