A High-Order Differential Equation Based Unsteady Wall Distance Solver

EasyChair Preprint 6306

Abstract

Wall-distance, defined as the distance from the closest surface, is used in the formulation of several turbulence modelling strategies like Detached Eddy Simulations or in turbulence models such as Spalart Allmaras and k-omega SST. In the current work, a solver is developed to compute wall distances based on the differential equations: Eikonal, Hamilton-Jacobi (H-J) and Poisson. The baseline solver, which employs first-order up-wind scheme for the spatial discretization of advection term, has been validated against several test cases. Subsequently, the upwind schemes are replaced with high order Explicit/Compact schemes upto 6th order accuracy. High-order schemes outperformed the accuracy of first order up-wind scheme when solving the H-J equation. Dispersion errors due to the hyperbolic nature of the Eikonal equation, as expected, has affected the wall-distance accuracy of high order schemes despite using a 10th order filter. The solver is further extended to compute unsteady wall distances, which is applicable to the flow simulations in which the walls/bodies are moving inside the computational domain. Results of an oscillating cube and a bouncing cube are demonstrated to be in agreement with the exact solution.

Keyphrases: Compact scheme, Eikonal, Hamilton-Jacobi, Poisson, Unsteady wall distance, Wall distance

@booklet{EasyChair:6306,
  author    = {Hemanth Chandra Vamsi Kakumani and Nagabhushana Rao Vadlamani},
  title     = {A High-Order Differential Equation Based Unsteady Wall Distance Solver},
  howpublished = {EasyChair Preprint 6306},
  year      = {EasyChair, 2021}}