Analysis of Slope Limiters on Irregular Grids

Abstract

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. Many slope limiters in standard use do not preserve linear solutions on irregular grids impacting both accuracy and convergence. We rewrite some well-known limiters to highlight their underlying symmetry, and use this form to examine the properties of both traditional and novel limiter formulations on non-uniform meshes. A consistent method of handling stretched meshes is developed which is both linearity preserving for arbitrary mesh stretchings and reduces to common limiters on uniform meshes. In multiple dimensions we analyze the monotonicity region of the gradient vector and show that the multidimensional limiting problem may be cast as the solution of a linear progranzming problem. For some special cases we present a new directional limiting formulation that preserves linear solutions in multiple dimensions on irregular grids. Computational results using model problems and complex three-dimensional examples are presented, demonstrating accuracy, monotonicity and robustness.

StreamFlow 1.0: an extension to the spatially distributed snow model Alpine3D for hydrological modelling and deterministic stream temperature prediction

“…Many slope limiters have been derived for regular space discretizations (LeVeque, 2002), but very few are available for irregular meshes (Berger et al, 2005;Zeng, 2013). StreamFlow implements the slope limiter developed by Zeng (2013),…”

“…Equation (16) is discretized over each stream reach using an explicit upwind finite volume scheme with second-order precision in space and first-order precision in time (Berger et al, 2005):…”

A Cell-Centered Multiphase ALE Scheme With Structural Coupling

“…However, Berger et al [65] recently showed improved results using a gradient-based approach. This method should be evaluated.…”

“…The limiter is applied to the gradient term, ∂w ∂x , in (2.86). The use of slope limiters is discussed in Toro [53], Berger et al [65], and Barth [66].…”

High Order Finite Elements for Lagrangian Computational Fluid Dynamics

“…The initial problem setup is illustrated in Figure 5.1. that we could make to improve the solution, such as implementing a monotonic slope limiter [3] or tuning of the qquad and qlin artificial viscosity coefficients.…”