An example of the Rvachev function method

TL;DR

This paper introduces a Rvachev function method combined with Chebyshev collocation for fluid flow stability analysis, offering a simpler alternative to traditional spectral methods that exactly satisfy boundary conditions without mesh generation.

Contribution

The paper presents a novel Rvachev function approach with Chebyshev collocation for stability analysis, eliminating the need for mesh generation and simplifying boundary condition handling.

Findings

Results agree well with reference data

Method is simpler than spectral/hp element method

Does not require mesh generation or geometric handling

Abstract

We present a Rvachev function method with the Chebysev collocation for the stability analysis of fluid flow. The strategy is to construct an approximate solution that satisfies all boundary conditions exactly. As an example, we consider the stability problem of the two-dimensional flow of an incompressible viscous liquid near a circular cylinder. The results coincide well with the reference data. The method is simpler than the widely used spectral/hp element method, in particular because it does not require mesh generation, and the collocation algorithm does not handle the boundary conditions or any geometric information.