A Study of Improved Limiter Formulations for Second-Order Finite Volume Schemes Applied to Unstructured Grids

TL;DR

This paper compares three limiter formulations in second-order finite volume schemes on unstructured grids for turbulent flow simulations, showing similar accuracy but different dissipation characteristics, validated against experimental data.

Contribution

It introduces a comparative analysis of three limiter formulations in finite volume schemes for unstructured grids, highlighting their dissipative behaviors and effectiveness in turbulent flow simulations.

Findings

All limiters produce similar results with proper control constants.

Different limiters exhibit distinct dissipative characteristics.

Numerical results agree well with experimental data.

Abstract

A general, compact way of achieving second-order in finite-volume numerical methods is to perform a MUSCL-like, piecewise linear reconstruction of flow properties at each cell interface. To avoid the surge of spurious oscillations in the discrete solution, a limiter function is commonly employed. This strategy, however, can add a series of drawbacks to the overall numerical scheme. The present paper investigates this behavior by considering three different limiter formulations in the context of a second-order, finite volume scheme for the simulation of steady, turbulent flows on unstructured meshes. Three limiter formulations are considered: the original Venkatakrishnan limiter, Wang's modification to the Venkatakrishnan limiter and Nishikawa's recently introduced R3 limiter. Three different configurations of the fully-developed, two-dimensional, transonic NACA 0012 airfoil are analyzed, configured with different angles of attack and similar freestream properties. The gas dynamics are modeled using the Reynolds-averaged Navier-Stokes (RANS) equations, where the negative Spalart-Allmaras turbulence model is used to solve the closure problem. All limiters are shown to yield similar results for all configurations of this case, although with different dissipative characteristics, provided their control constants are used within appropriate intervals. The presented numerical results are in good agreement with experimental data available in the literature.