Highly accurate compact flowfield dependent variation method for solving two-dimensional navier-stokes equations - Elfagi, Abdulhafid M.; Ahmed Omer, Elhassen Ali; Asrar, Waqar; Omar, Ashraf Ali (2011)
A higher order accurate method, namely high order compact flowfield dependent variation (HOC-FDV) method, has been developed to solve full Navier-Stokes equations. The 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-dimensional numerical examples are tested to examine the accuracy and shockwave boundary layer interactions. The results showed the high accuracy and the capability of the higher order scheme to simulate accurately the separation and discontinuity