A high order Spectral Volume method for moving boundary problems

Abstract

In this paper, we obtain inherently unsteady solutions to the Navier-Stokes equations involving moving boundaries. We employ a mapping function to map the grid and the flow features between a fixed reference frame and a moving reference frame. The actual equations of conservation (applicable on the moving reference frame) are then rewritten so as to form an altered set of equations, which are valid in the fixed reference frame. These altered set of equations are discretized and then solved using the high order spectral volume method (SV). The time advancement is carried out using the three stage Runge Kutta method. Simulations are performed to demonstrate the proof of the above concept and the ability of this method to handle more complicated motions.