scholarly journals Marker Re-Distancing (MRD) Algorithm for High-Fidelity Interface Tracking on Arbitrary Meshes

2017 ◽  
Author(s):  
Patrick T. Greene ◽  
Robert Nourgaliev ◽  
Samuel P. Schofield
Keyword(s):  
Material Flow ◽  
High Order ◽  
Interface Tracking ◽  
High Fidelity ◽  
Time Step ◽  
Tracking Method ◽  
Flow Problems ◽  
Constrained Minimization Problem ◽  
Irregular Meshes ◽  
Stability Time

A new sharp high-order interface tracking method for multi-material flow problems on unstructured meshes is presented. This marker re-distancing (MRD) method is designed to work accurately and robustly on unstructured, generally highly distorted meshes, necessitated by applications within ALE-based hydrocodes. The method is a hybrid of a Lagrangian marker tracking method and a novel discontinuous Galerkin (DG) projection based level set re-distancing algorithm. The re-distancing method is formulated as a constrained minimization problem and is shown to obtain arbitrary orders of convergence for smooth interfaces. High-order (>2nd) re-distancing on irregular meshes is a must for applications were the interfacial curvature is important for the underlying physics, such as surface tension, wetting, and detonation shock dynamics. Since no PDE is solved for re-distancing, the method does not have a stability time step restriction, which is particularly useful in combination with AMR, used here to efficiently resolve fine interface features. In addition, the method can robustly handle discontinuities in the distance function without explicit utilization of solution limiters. Results will be shown for a number of different interface geometries, which will demonstrate the method’s capability of obtaining high-fidelity results on arbitrary meshes.

scholarly journals Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1799
Author(s):  
Irene Gómez-Bueno ◽  
Manuel Jesús Castro Díaz ◽  
Carlos Parés ◽  
Giovanni Russo
Keyword(s):  
High Order ◽  
Collocation Methods ◽  
Quadrature Formulas ◽  
Balance Laws ◽  
Source Terms ◽  
Time Step ◽  
Systems Of Balance Laws ◽  
Reconstruction Operator ◽  
Non Linear ◽  
Linear Problems

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

scholarly journals A high-fidelity realization of the Euclid code comparison N-body simulation with Abacus

2019 ◽  
Vol 485 (3) ◽  
pp. 3370-3377 ◽  
Author(s):  
Lehman H Garrison ◽  
Daniel J Eisenstein ◽  
Philip A Pinto
Keyword(s):  
Power Spectrum ◽  
High Performance ◽  
High Fidelity ◽  
Step Size ◽  
Time Step ◽  
Code Comparison ◽  
Force Accuracy ◽  
Integration Errors ◽  
Better Than ◽  
Good Agreement

Abstract We present a high-fidelity realization of the cosmological N-body simulation from the Schneider et al. code comparison project. The simulation was performed with our AbacusN-body code, which offers high-force accuracy, high performance, and minimal particle integration errors. The simulation consists of 20483 particles in a $500\ h^{-1}\, \mathrm{Mpc}$ box for a particle mass of $1.2\times 10^9\ h^{-1}\, \mathrm{M}_\odot$ with $10\ h^{-1}\, \mathrm{kpc}$ spline softening. Abacus executed 1052 global time-steps to z = 0 in 107 h on one dual-Xeon, dual-GPU node, for a mean rate of 23 million particles per second per step. We find Abacus is in good agreement with Ramses and Pkdgrav3 and less so with Gadget3. We validate our choice of time-step by halving the step size and find sub-percent differences in the power spectrum and 2PCF at nearly all measured scales, with ${\lt }0.3{{\ \rm per\ cent}}$ errors at $k\lt 10\ \mathrm{Mpc}^{-1}\, h$. On large scales, Abacus reproduces linear theory better than 0.01 per cent. Simulation snapshots are available at http://nbody.rc.fas.harvard.edu/public/S2016.

Modeling of Material Flow Problems

2017 ◽  
pp. 21-36 ◽  
Author(s):  
Simone Göttlich ◽  
Michael Herty ◽  
Melanie Luckert
Keyword(s):  
Material Flow ◽  
Flow Problems

High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method

2012 ◽  
Vol 12 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Thibault Pringuey ◽  
R. Stewart Cant
Keyword(s):  
Level Set ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
High Order ◽  
Convex Polyhedra ◽  
Two Phase ◽  
High Order Schemes ◽  
Flow Problems ◽  
Mixed Element ◽  
Areas Of Interest

AbstractIn this article, we detail the methodology developed to construct arbitrarily high order schemes — linear and WENO — on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.

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