Improved Wall-Normal Derivative Formulae for Anisotropic Adaptive Simplex-Element Grids

TL;DR

This paper introduces improved methods for calculating wall-normal derivatives on unstructured simplex-element grids, reducing numerical noise and enhancing accuracy in fluid dynamics simulations involving wall shear and heat transfer.

Contribution

It proposes a novel finite-difference approach with a common step-length and explores least-squares gradients to improve derivative accuracy on irregular grids.

Findings

Reduced noise in wall-normal derivatives on irregular grids

Enhanced accuracy of derivative calculations

Effective for anisotropic adaptive simplex-element grids

Abstract

In this paper, we explore methods for computing wall-normal derivatives used for calculating wall skin friction and heat transfer over a solid wall in unstructured simplex-element (triangular/tetrahedral) grids generated by anisotropic grid adaptation. Simplex-element grids are considered as efficient and suitable for automatic grid generation and adaptation, but present a challenge to accurately predict wall-normal derivatives. For example, wall-normal derivatives computed by a simple finite-difference approximation, as typically done in practical fluid-dynamics simulation codes, are often contaminated with numerical noise. To address this issue, we propose an improved method based on a common step-length for the finite-difference approximation, which is otherwise random due to grid irregularity and thus expected to smooth the wall-normal derivative distribution over a boundary. Also, we consider using least-squares gradients to compute the wall-normal derivatives and discuss their possible improvements. Numerical results show that the improved methods greatly reduce the noise in the wall-normal derivatives for irregular simplex-element grids.