Computational evaluation of convection schemes in fluid dynamics problems

TL;DR

This paper evaluates high-resolution convection schemes in fluid dynamics using computational methods, comparing their performance on nonlinear problems and applying the best scheme to 3D free surface flow simulations.

Contribution

It provides a comparative analysis of WACEB, CUBISTA, and ADBQUICKEST schemes for nonlinear fluid problems and demonstrates their application in complex 3D flows.

Findings

WACEB, CUBISTA, and ADBQUICKEST schemes are ranked based on performance.

The best scheme effectively simulates 3D free surface flows.

The analysis guides the selection of convection schemes for nonlinear fluid dynamics.

Abstract

This article provides a computational evaluation of the popular high resolution upwind WACEB, CUBISTA and ADBQUICKEST schemes for solving non-linear fluid dynamics problems. By using the finite difference methodology, the schemes are analyzed and implemented in the context of normalized variables of Leonard. In order to access the performance of the schemes, Riemann problems for 1D Burgers, Euler and shallow water equations are considered. From the numerical results, the schemes are ranked according to their performance in solving these non-linear equations. The best scheme is then applied in the numerical simulation of tridimensional incompressible moving free surface flows.