Stability analysis and error estimate of flowfield-dependent variation (FDV) method for first order linear hyperbolic equations

Flowfield-dependent variation (FDV) method has been used in fluid mechanics and astrophysics. This method has been developed to solve many flow problems such as the interactions of shock waves with turbulent boundary layers in transonic flow and hypersonic flow, and chemically reacting flows. However, stability analysis and error estimate are missing in the numerical method. In this paper we analyze FDV method for a first-order linear hyperbolic equation, and apply finite difference method to discretize the space variable. Stability conditions and optimal error estimates are proved.