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A computationally efficient high-order solver is developed to compute thewall distances by solving the relevant partial differential equations, namely:Eikonal, Hamilton-Jacobi (HJ) and Poisson equations. In contrast to the upwindschemes widely used in the literature, we explore the suitability of high-ordercentral difference schemes (explicit/compact) for the wall-distancecomputation. While solving the Hamilton-Jacobi equation, the high-order centraldifference schemes performed approximately $1.4-2.8$ times faster than theupwind schemes with a marginal improvement in the solution accuracy. A newpseudo HJ formulation based on the localized artificial diffusivity (LAD)approach has been proposed. It is demonstrated to predict results with anaccuracy comparable to that of the Eikonal equation and the simulations are$\approx$ 1.5 times faster than the baseline HJ solver using upwind schemes. Acurvature correction is also incorporated in the HJ equation to correct for thenear-wall errors due to concave/convex wall curvatures. We demonstrate theefficacy of the proposed methods on both the steady and unsteady test cases andexploit the unsteady wall-distance solver to estimate the instantaneous shapeand burning surface area of a dendrite propellant grain in a solid propellantrocket motor.

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