AMROC's WENO-TCD Method with LES Capability - Documentation

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

$\frac{d f}{d x} = \frac{1}{h} \big(\beta(f_{i+1}-f_{i-1})+\alpha (f_{i+2}-f_{i-2}) \big)$

where $\beta = 1/2-2 \alpha$ and $\alpha=-0.197$ . This value of $\alpha$ is obtained by minimizing the truncation errors that result for flows with a Kolmogorov-like spectra.