The purpose of the WENO-TCD integrator is to provide a fluid dynamics solver in AMROC that brings together the numerical requirements of simulating flows with strong shocks/discontinuities and turbulence. In the first case, unresolvable discontinuities are handled by shock capturing methods. In the second case, the turbulent regions can only be computed accurately using low dissipation (zero if possible) numerical methods. This is accomplished by upwinding the derivatives around discontinuities and using centered schemes around the turbulent regions of the flow. The current solver uses a switched paradigm, in which a user defined criteria determines when to use a centered or upwind method. Additionaly, we implement the solver as a flux based method that enables switching numerical schemes mantaining discrete conservation (important in order to compute the correct speed of discontinuities). The scheme is defined by the 5 point stensil formula

where
and
. This value of
is obtained by minimizing the truncation errors that result for flows with a Kolmogorov-like spectra.
Related papers are:
- Hill & Pullin (2004), "Hybrid tuned center difference - WENO method for Large-Eddy Simulation in the presence of strong shocks", Journal of Computational Physics, 194(2), 435-450.
- Liu, Osher & Chan (1994) "Weighted essenctially nonoscillatory schemes", Journal of Computational Physics, 115(1), 200-212.
- Misra & Pullin (1997) "A vortex-based subgrid model for large-eddy simulation", Physics of Fluids, 9(8), 2443-2454.
- Pullin (2000) "Vortex-based model for subgrid flux of a passive scalar", Physics of Fluids, 12(9), 2311-2319.
- Pantano, Deiterding, Hill & Pullin (2006), "A low-numerical dissipation patched-based adaptive mesh refinement method for large-eddy simulation of compressible flows", Journal of Computational Physics.
Several examples are documented for this method.