On the use of high order central difference schemes for differential equation based wall distance computations

A computationally efficient high-order solver is developed to compute the wall distances by solving relevant partial differential equations, namely: Eikonal, Hamilton–Jacobi (HJ) and Poisson equations. In contrast upwind schemes widely used in literature, we explore suitability of central difference (explicit/compact) for wall-distance computation. While equation, performed approximately 1.4–2.8 times faster than with a marginal improvement solution accuracy. new pseudo HJ formulation based on localized artificial diffusivity (LAD) approach has been proposed. It demonstrated predict results an accuracy comparable that Eikonal equation simulations are ? 1.5 baseline using schemes. curvature correction also incorporated correct near-wall errors due concave/convex curvatures. We demonstrate efficacy proposed methods both steady unsteady test cases exploit estimate instantaneous shape burning surface area dendrite propellant grain solid rocket motor.