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We provide a method to compute the entropy-satisfying weak solution to theeikonal equation in an arbitrary-order polynomial space. The method uses anartificial viscosity approach and is demonstrated for the signed distancefunction, where exact solutions are available. The method is designedspecifically for an existing high-order discontinuous-Galerkin framework, whichuses standard convection, diffusion, and source terms. We show design order ofaccuracy and good behavior for both shocks and rarefaction type solutions.Finally the distance function around a complex multi-element airfoil iscomputed using a high-order-accurate representation.

Arbitrary Order Solutions for the Eikonal Equation using a Discontinuous Galerkin Method