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

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.