AN INTERPOLATION TECHNIQUE FOR THE METHOD OF CHARACTERISTICS IN 4-DIMENSIONS DOMAIN

Gamal Hafez

doi:10.53370/001c.23738

Abstract

An interpolation procedure for unsteady inviscid flow (i.e. Euler) solvers is developed. The proposed linear interpolation is first order accurate in time (Δt). The flow properties at each non-mesh point are interpolated in a physical manner as a summation of the values at its surrounding eight mesh points multiplied by their respective weighting coefficients. The coefficients are based on the distances apart between the interpolating non-mesh point and the eight mesh points. The major advantage in this technique is using the position vector for interpolation instead of using the three coordinates x, y & z in succession. This means that it is a one step interpolation instead of three steps. Finally, the compatibility is achieved from using the hyper characteristic curves to locate the initial data points. The proposed technique offers an accurate, efficient and compatible interpolation valid for the method of characteristics in 4-D.

Highlights

Careful implementation of solution methods in computational fluid dynamics has become recently more important
An attempt to develop an interpolation technique and to avoid using polynomials for the interpolation is demonstrated in the present paper
The present interpolation technique successfully avoids the use of polynomials, which govern the distribution between the mesh points in non-physical manner

Summary

INTRODUCTION

Careful implementation of solution methods in computational fluid dynamics has become recently more important. For the solution of Navier-Stokes equations, the method of characteristics in 4-D was applied to the hyperbolic part [3]. In this method, an interpolation technique is necessary to obtain the initial conditions and to maintain the solution stability. The direct expansion of the last one for the solution of three-dimension unsteady flow field leads to a very long threestep first order interpolation technique. An attempt to develop an interpolation technique and to avoid using polynomials for the interpolation is demonstrated in the present paper. Following this introduction, the main equations and their solution are presented.

CHARACTERISTIC EQUATIONS

PROPOSED INTERPOLATION TECHNIQUE

TEST MODEL

CONCLUSIONS