The q-least squares kinetic upwind method (q-LSKUM) with variable step applied to internal fluid flow problems

In any fluid flow calculation. it is essential to capture the finer details of the flow field to obtain a high degree of accuracy in the flow quantiti es (density, velocity and pressure). It is therefore necessary to have a fi ner grid in the region where the solution is varying very rapidly and coars er grid in regions where the solution is smooth. In fact, this helps to avo id unnecessary computations to a great extent. In this paper we use the q-L SKUM in order to solve a transonic flow for a channel with a bump. We gener ate the grid by using the elliptic grid generation technique. The method is meant for constructing a boundary-fitted coordinate system around a body o f arbitrary shape. The nodes are then clustered at the shock location using a simple method of grid stretching. The Euler equations are solved at each of the coordinates (x,y) thus obtained using the q-LSKUM. (C) 2001 Elsevie r Science B.V. All rights reserved.