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

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 quantities (density, velocity and pressure). It is therefore necessary to have a finer grid in the region where the solution is varying very rapidly and coarser grid in regions where the solution is smooth. In fact, this helps to avoid unnecessary computations to a great extent. In this paper we use the q-LSKUM in order to solve a transonic flow for a channel with a bump. We generate the grid by using the elliptic grid generation technique. The method is meant for constructing a boundary-fitted coordinate system around a body of 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.