High-Throughput TVD-Based Simulation of Tracer Flow

Abstract

Abstract High-throughput, total-variation-diminishing based, numerical techniques for simulating tracer flow are developed. High-throughput (HT) timestepping enables explicit differencing techniques to use timesteps that are larger than allowed by normal stability constraints. Total-variation-diminishing (TVD) based techniques are a means of controlling the solution oscillations associated with high-order differencing schemes. The concept of ‘upstream stability’ is introduced to help combine HT timestepping with TVD-based differencing. Additionally, an improved HT timestepping algorithm for solving physically dispersive flow problems is developed. Numerical experiments indicate that HT timestepping is most beneficial for solving highly convective flows that have both a physical Peclet number and a diffusion-only numerical Peclet number greater than one. Experiments comparing standard and alternating direction TVD-based techniques with both the Superbee (SB) and third-order based (L3) limiters indicate that the TVD-SB scheme is the most accurate for purely convective problems. For physically dispersive problems, the TVD-SB scheme may be too compressive and the TVD-L3 is recommended. The alternating direction TVD scheme is the least sensitive to timestepping and the most sensitive to grid-orientation.