Purpose
– The purpose of this paper is to investigate the computational features of the Flowfield Dependent Variation (FDV) method, a numerical scheme built to simulate flows characterized by multiple speeds, multiple physical phenomena, and by large variations in flow variables.
Design/methodology/approach
– Fundamentally, the FDV method may be regarded as a variant of the Lax-Wendroff Scheme (LWS) that is obtained by replacing the explicit time derivatives in LWS by a weighted combination of explicit and implicit time derivatives. The weighting factors – referred to as FDV parameters – may be broadly classified as convective and diffusive parameters which, for example, are determined using flow quantities such as the Mach number and Reynolds number, respectively. Hence, the reference to these parameters and the method as “flow field dependent.” A von Neumann Fourier analysis demonstrates that the increased implicitness makes FDV both more stable and less dispersive compared to LWS, a feature crucial to capturing shocks and other phenomena characterized by high gradients in variables. In the current study, the FDV scheme is implemented in a Taylor-Galerkin-based finite element method framework that supports arbitrarily high order, unstructured isoparametric elements in one-, two- and three-dimensional geometries.
Findings
– At first, the spatial accuracy of the implemented FDV scheme is established using the Method of Manufactured Solutions, wherein the results show that the order of accuracy of the scheme is nearly equal to the order of the shape function polynomial plus one. The dispersion and dissipation errors of FDV, when applied to the compressible Navier-Stokes and energy equations, are investigated using a 2-D, small-amplitude acoustic pulse propagating in a quiescent medium. It is shown that FDV with third-order shape functions accurately captures both the amplitude and phase of the acoustic pulse. The method is then applied to cases ranging from low-Mach number subsonic flows (Mach number M=0.05) to high-Mach number supersonic flows (M=4) with shock-boundary layer interactions. For all cases, fair to good agreement is observed between the current results and those in the literature.
Originality/value
– The spatial order of accuracy of the FDV method, its stability and dispersive properties, as well as its applicability to low- and high-Mach number flows are established.
Applications of Overset Grid Technique to CFD Simulation of High Mach Number Multi-body Interaction/Separation Flow
