A high order differential equation based wall distance solver

A computationally efficient high-order solver is developed to compute the wall distances, which are typically used for turbulence modelling, peripheral flow simulations, Computer Aided Design (CAD) etc. The wall distances are computed by solving the differential equations namely: Eikonal, Hamilton-Jacobi (H-J) and Poisson. The computational benefit of using high-order schemes (explicit/compact schemes) for wall-distance solvers, both in terms of accuracy and computational time, has been demonstrated. A new H-J formulation based on the localized artificial diffusivity (LAD) approach has been proposed, which has produced results with an accuracy comparable to that of the Eikonal formulation. When compared to the baseline H-J solver using upwind schemes, the solution accuracy has improved by an order of magnitude and the calculations are $\approx$ 5 times faster using the modified H-J formulation. A modified curvature correction has also been implemented into the H-J solver to account for the near-wall errors due to concave/convex wall curvatures. The performance of the solver using different schemes has been tested both on the steady canonical test cases and the unsteady test cases like `piston-cylinder arrangement', `bouncing cube' and `burning of a star grain propellant' where the wall-distance evolves with time.