RICH: OPENSOURCE HYDRODYNAMIC SIMULATION ON A MOVING VORONOI MESH
Abstract
We present here RICH, a stateoftheart twodimensional hydrodynamic code based on Godunov’s method, on an unstructured moving mesh (the acronym stands for Racah Institute Computational Hydrodynamics). This code is largely based on the code AREPO. It differs from AREPO in the interpolation and timeadvancement schemeS as well as a novel parallelization scheme based on Voronoi tessellation. Using our code, we study the pros and cons of a moving mesh (in comparison to a static mesh). We also compare its accuracy to other codes. Specifically, we show that our implementation of external sources and timeadvancement scheme is more accurate and robust than is AREPO when the mesh is allowed to move. We performed a parameter study of the cell rounding mechanism (Lloyd iterations) and its effects. We find that in most cases a moving mesh gives better results than a static mesh, but it is not universally true. In the case where matter moves in one way and a sound wave is traveling in the other way (such that relative to the grid the wave is not moving) a static mesh gives better results than a moving mesh. We perform an analytic analysis for finite difference schemes that reveals that a Lagrangianmore »
 Authors:
 Racah Institute of Physics, The Hebrew University, 91904, Jerusalem (Israel)
 Publication Date:
 OSTI Identifier:
 22340087
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astrophysical Journal, Supplement Series; Journal Volume: 216; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; ALGORITHMS; ANALYTIC FUNCTIONS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; HYDRODYNAMICS; INTERPOLATION; LAGRANGIAN FUNCTION; SOUND WAVES; SUPERSONIC FLOW; TWODIMENSIONAL CALCULATIONS
Citation Formats
Yalinewich, Almog, Steinberg, Elad, and Sari, Re’em. RICH: OPENSOURCE HYDRODYNAMIC SIMULATION ON A MOVING VORONOI MESH. United States: N. p., 2015.
Web. doi:10.1088/00670049/216/2/35.
Yalinewich, Almog, Steinberg, Elad, & Sari, Re’em. RICH: OPENSOURCE HYDRODYNAMIC SIMULATION ON A MOVING VORONOI MESH. United States. doi:10.1088/00670049/216/2/35.
Yalinewich, Almog, Steinberg, Elad, and Sari, Re’em. 2015.
"RICH: OPENSOURCE HYDRODYNAMIC SIMULATION ON A MOVING VORONOI MESH". United States.
doi:10.1088/00670049/216/2/35.
@article{osti_22340087,
title = {RICH: OPENSOURCE HYDRODYNAMIC SIMULATION ON A MOVING VORONOI MESH},
author = {Yalinewich, Almog and Steinberg, Elad and Sari, Re’em},
abstractNote = {We present here RICH, a stateoftheart twodimensional hydrodynamic code based on Godunov’s method, on an unstructured moving mesh (the acronym stands for Racah Institute Computational Hydrodynamics). This code is largely based on the code AREPO. It differs from AREPO in the interpolation and timeadvancement schemeS as well as a novel parallelization scheme based on Voronoi tessellation. Using our code, we study the pros and cons of a moving mesh (in comparison to a static mesh). We also compare its accuracy to other codes. Specifically, we show that our implementation of external sources and timeadvancement scheme is more accurate and robust than is AREPO when the mesh is allowed to move. We performed a parameter study of the cell rounding mechanism (Lloyd iterations) and its effects. We find that in most cases a moving mesh gives better results than a static mesh, but it is not universally true. In the case where matter moves in one way and a sound wave is traveling in the other way (such that relative to the grid the wave is not moving) a static mesh gives better results than a moving mesh. We perform an analytic analysis for finite difference schemes that reveals that a Lagrangian simulation is better than a Eulerian simulation in the case of a highly supersonic flow. Moreover, we show that Voronoibased moving mesh schemes suffer from an error, which is resolution independent, due to inconsistencies between the flux calculation and the change in the area of a cell. Our code is publicly available as open source and designed in an objectoriented, userfriendly way that facilitates incorporation of new algorithms and physical processes.},
doi = {10.1088/00670049/216/2/35},
journal = {Astrophysical Journal, Supplement Series},
number = 2,
volume = 216,
place = {United States},
year = 2015,
month = 2
}

We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finitevolume form. The meshgenerating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and nonrelativistic fluidsmore »

Lagrangian method for the shallow water equations based on a Voronoi meshone dimensional results
A Lagrangian method for the Shallow Water equations in one dimension is presented. The method is based on the following idea. Place N points on a line to represent the fluid. Each point represent all the fluid that is closer to this point than to any other. This partitions the line into intervals. The principle of Least Action yields a set of difference equations which can be easily solved at each time step to give new values for the height and velocity of the fluid particles in each interval. The points are then moved to their new locations and themore » 
Deformation behavior of particlestrengthened alloys: A Voronoi mesh approach
A modelling approach based on the discretization of a particlestrengthened material using a Voronoi mesh is considered. The model is applied to studying the effects of particle arrangement on the deformation behavior of a particlestrengthened alloy, particularly on its creep resistance. On a local scale, i.e., within an individual Voronoi cell containing a single particle, a dislocation densitybased constitutive model developed previously is applied. Interaction with adjacent Voronoi cells due to plastic incompatibilities is also included. The model predicts a dependence of the creep resistance on the character of particle distribution, notably, on the degree of particle clustering. Application tomore » 
MeshVoro: A ThreeDimensional Voronoi Mesh Building Tool for the TOUGH Family of Codes
Few tools exist for creating and visualizing complex threedimensional simulation meshes, and these have limitations that restrict their application to particular geometries and circumstances. Mesh generation needs to trend toward ever more general applications. To that end, we have developed MeshVoro, a tool that is based on the Voro (Rycroft 2009) library and is capable of generating complex threedimensional Voronoi tessellationbased (unstructured) meshes for the solution of problems of flow and transport in subsurface geologic media that are addressed by the TOUGH (Pruess et al. 1999) family of codes. MeshVoro, which includes builtin data visualization routines, is a particularly usefulmore » 
Construction of the Voronoi mesh on a sphere
A new construction of the Voronoi mesh on the sphere is presented. The main feature is that the algorithm adds points one at a time until the final Voronoi mesh is built up. By adding one point to an existing Voronoi mesh of K points, only local changes are needed to construct a Voronoi mesh of K+1 points. This construction is particularly well suited to timedependent problems since using information from the Voronoi mesh at the previous time step allows us to reduce the construction to O(N) operations when the two configurations are close, while the algorithm does not breakmore »