Higher-Order Compact-Flow Field-Dependent Variation (HOC-FDV) Method for Solving Two-Dimensional Navier-Stokes Equations

Abstract

In this article, a new, higher-order accurate method, namely higher-order compact-flow field-dependent variation (HOC-FDV) method, has been developed to solve two-dimensional Navier-Stokes equations. The HOC-FDV scheme is of third-order accuracy in time and fourth-order in space. The spatial derivatives in the flow field-dependent variation (FDV) equations proposed by Chung are approximated using higher-order compact (HOC) Hermitian (Pade) scheme. The solution procedure at each time step consists of a system of block tri-diagonal matrices which can be solved efficiently in a standard manner. Several numerical examples are tested to examine the accuracy and capability of the new scheme to capture the shock and to simulate accurately separation and discontinuity.

Keywords:

• Navier Stokes Equations
• Flow Field-Dependent Variation Method (FDV)
• Higher-Order Compact Schemes (HOC)
• Shock Capturing
• Viscous Flow