Unsteady flow computations for flow past multiple moving boundaries using LSKUM

We present the latest developments in the least squares kinetic upwind method (LSKUM), a kinetic theory based grid free approach for the solution of Euler equations. A single step higher order scheme through modified CIR splitting is presented. A new weighted least squares method has been used in the present work which simplifies the 2-D formulae to an equivalent 1-D form. This is achieved through diagonalisation of the least squares matrix through suitable choices of the weights. All these developments have been extended to problems with moving nodes and boundaries. A 2-D unsteady Euler code has been developed incorporating all the above ideas along with the well known dual time stepping procedure. The code has been verified and validated for the standard test case AGARD CT(5) which corresponds to unsteady flow past oscillating NACA0012 airfoil pitching about quarter chord. Good comparisons with the experimental values have been obtained. In order to demonstrate the ability of the method to handle multiple moving bodies we have computed unsteady flow past two oscillating NACA0012 airfoils one behind the other. Some interesting results are presented for this case.