Higher order compact-flowfield dependent variation (HOCFDV) method for solving navier-stokes equations - Elfaghi, Abdulhafid M.; Asrar, Waqar; Omar, Ashraf Ali E. (2010)
In this paper, a novel high order accurate method, namely high order compact flowfield dependent variation (HOC-FDV) method, has been developed to solve full Navier Stokes equations. The new scheme is a third order accuracy in time and fourth order accuracy in space. The spatial derivatives in the third order accuracy in time, flowfield dependent variation (FDV) equations proposed by Chung, are approximated using high order compact (HOC) Hermitian (Pade) scheme. The solution procedure at each time step consists of a system of block tri-diagonal matrix which can be solved efficiently in a standard manner. Two numerical examples namely; shock tube (Sod) problem and supersonic flow over a flat plate are tested to examine the accuracy and shockwave boundary layer interaction. The results showed the high accuracy and the capability of the new scheme to capture the shock and to simulate accurately the separation and discontinuity.