Reducing numerical diffusion in interfacial gravity wave simulations

We demonstrate how the background potential energy is an excellent measure of the effective numerical diffusion or antidiffusion of an advection scheme by applying several advection schemes to a standing interfacial gravity wave. All existing advection schemes do not maintain the background potential energy because they are either diffusive, antidiffusive, or oscillatory. By taking advantage of the compressive nature of some schemes, which causes a decrease in the background potential energy, and the diffusive nature of others, which causes an increase in the background potential energy, we develop two background potential energy preserving advection schemes that are well-suited to study interfacial gravity waves at a density interface between two miscible fluids in closed domains such as lakes. The schemes employ total variation diminishing limiters and universal limiters in which the limiter is a function of both the upwind and local gradients as well as the background potential energy. The effectiveness of the schemes is validated by computing a sloshing interfacial gravity wave with a nonstaggered-grid Boussinesq solver, in which QUICK is employed for momentum and the pressure correction method is used, which is second-order accurate in time. For scalar advection, the present background potential energy preserving schemes are employed and compared to other TVD and non-TVD schemes, and we demonstrate that the schemes can control the change in the background potential energy due to numerical effects. Copyright (c) 2005 John Wiley & Sons, Ltd.