Burgers_1D

Burgers_1D copied to clipboard

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.