3D Adaptive Central Schemes: part I Algorithms for Assembling the Dual Mesh

TL;DR

This paper introduces a novel 3D adaptive finite volume scheme on Cartesian grids that efficiently constructs dual meshes using Voronoi cells, enabling faster computations for flow simulations.

Contribution

It presents a new method for assembling dual meshes in 3D adaptive grids using Voronoi cells, improving computational efficiency and precomputability.

Findings

Efficient dual mesh construction using Voronoi cells.

Precomputable geometric information for rapid scheme execution.

Comparison shows reduced complexity and effort.

Abstract

Central schemes are frequently used for incompressible and compressible flow calculations. The present paper is the first in a forthcoming series where a new approach to a 2nd order accurate Finite Volume scheme operating on cartesian grids is discussed. Here we start with an adaptively refined cartesian primal grid in 3D and present a construction technique for the staggered dual grid based on $L^{\infty}$-Voronoi cells. The local refinement constellation on the primal grid leads to a finite number of uniquely defined local patterns on a primal cell. Assembling adjacent local patterns forms the dual grid. All local patterns can be analysed in advance. Later, running the numerical scheme on staggered grids, all necessary geometric information can instantly be retrieved from lookup-tables. The new scheme is compared to established ones in terms of algorithmical complexity and computational effort.