A normal ray refinement technique for Cartesian-grid based Navier–Stokes solvers

Abstract

In this work, a novel technique called normal ray refinement (NRR) is developed, implemented and investigated. Normal ray refinement is designed to allow for the viscous fluid flow simulations using an unstructured Cartesian grid framework in a computationally efficient manner. A key benefit of using a Cartesian grid method is that the grid can be automatically generated, thereby saving a vast amount of time and effort for complex geometries. The main drawback of using the Cartesian grid method is the large number of cells required to resolve viscous boundary layers, and it is this problem that the NRR approach addresses. The NRR approach relies on the use of refined normal rays of cells emanating from the body surface and spanning the boundary layer. Separating these rays along the body surface are relatively large cells too coarse to accurately capture viscous gradients. The heart of the NRR approach lies in the inter-ray communication strategies used between the normal rays that allow the accurate simulation of boundary layers even though the cells separating the rays are large. This yields a large reduction in the number of cells in the grid, which reduces the computational cost of simulation. This paper provides a background on different viscous Cartesian grid-based methods, followed by an explanation of the NRR approach, then some initial 2D results obtained using NRR for Reynolds numbers up to 1 million. It is shown that NRR can yield substantial reduction in computational cost relative to the standard Cartesian approach.