Profile-modifiable Conservative Transport Schemes and a Simple Multi-integrated Moment Formulation for Hydrodynamics

Abstract

This paper introduces a class of conservative transport schemes (CIP-CSL), which combines an Eulerian conservative formulation with a semi-Lagrangian solution procedure. Emphasis is particularly placed on the implementations of the methods to various fluid dynamic problems. One of the schemes can be directly used as an interface tracking method for multi-fluid computation by modifying the slope of the reconstructed interpolation. A simple methodology based on multi-integrated moment, namely VSIA, is also presented. VSIA (Volume Surface Integrated Average) method employs two integrated moments which are called VIA (Volume Integrated Average) and SIA (Surface Integrated Average), and gives a completely conservative formulation for the VIA. The numerical model is based on the CIP-CSL schemes and can be constructed under a lucid guideline. Some numerical aspects of the VSIA for general evolution equations will be briefly discussed, and implementations for inviscid compressible flow and incompressible viscous flow will be then presented.