Spectral Volume Method: application to Euler equations and performance appraisal

The compact high-order "Spectral Volume Method" designed for conservation laws on unstructured grids is presented. Its spectral reconstruction is exposed briefly and its applications to the Euler equations are presented through several test cases to assess its accuracy and stability. Comparisons with usual methods such as MUSCL show the superiority of SVM. The SVM method arises as a high-order accurate scheme, geometrically flexible and computationally efficient

Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh

Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi) Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equations and has been realized in the AREPO code both in 2D and 3D. We propose a new approach to compute accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a finite volume solver of the Navier-Stokes equations. Through a number of test problems, including circular Couette flow and flow past a cylindrical obstacle, we show that our new scheme combines good accuracy with geometric flexibility, and hence promises to be competitive with other highly refined Eulerian methods. This will in particular allow astrophysical applications of the AREPO code where physical viscosity is important, such as in the hot plasma in galaxy clusters, or for viscous accretion disk models.Comment: 26 pages, 21 figures. Submitted to MNRA

A multidimensional hydrodynamic code for structure evolution in cosmology

A cosmological multidimensional hydrodynamic code is described and tested. This code is based on modern high-resolution shock-capturing techniques. It can make use of a linear or a parabolic cell reconstruction as well as an approximate Riemann solver. The code has been specifically designed for cosmological applications. Two tests including shocks have been considered: the first one is a standard shock tube and the second test involves a spherically symmetric shock. Various additional cosmological tests are also presented. In this way, the performance of the code is proved. The usefulness of the code is discussed; in particular, this powerful tool is expected to be useful in order to study the evolution of the hot gas component located inside nonsymmetric cosmological structures.Comment: 34 pages , LaTex with aasms4.sty, 7 postscript figures, figure 4 available by e-mail, tared , gziped and uuencoded. Accepted Ap

FullSWOF_Paral: Comparison of two parallelization strategies (MPI and SKELGIS) on a software designed for hydrology applications

In this paper, we perform a comparison of two approaches for the parallelization of an existing, free software, FullSWOF 2D (http://www. univ-orleans.fr/mapmo/soft/FullSWOF/ that solves shallow water equations for applications in hydrology) based on a domain decomposition strategy. The first approach is based on the classical MPI library while the second approach uses Parallel Algorithmic Skeletons and more precisely a library named SkelGIS (Skeletons for Geographical Information Systems). The first results presented in this article show that the two approaches are similar in terms of performance and scalability. The two implementation strategies are however very different and we discuss the advantages of each one.Comment: 27 page

Assessment of the Spectral Volume Method on inviscid and viscous flows

The compact high-order "Spectral Volume Method" designed for conservation laws on unstructured grids is presented. Its spectral reconstruction is exposed briefly and its applications to the Euler equations are presented through several test cases to assess its accuracy and stability. Comparisons with classical methods such as MUSCL show the superiority of SVM. The SVM method arises as a high-order accurate scheme, geometrically flexible and computationally efficient

SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics

We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers. The robustness of the discontinuous Galerkin method allows for the use of high-resolution shock capturing methods in regions where (relativistic) shocks are found, while exploiting high-order accuracy in smooth regions. A task-based parallelism model allows efficient use of the largest supercomputers for problems with a heterogeneous workload over disparate spatial and temporal scales. We argue that the locality and algorithmic structure of discontinuous Galerkin methods will exhibit good scalability within a task-based parallelism framework. We demonstrate the code on a wide variety of challenging benchmark problems in (non)-relativistic (magneto)-hydrodynamics. We demonstrate the code's scalability including its strong scaling on the NCSA Blue Waters supercomputer up to the machine's full capacity of 22,380 nodes using 671,400 threads.Comment: 41 pages, 13 figures, and 7 tables. Ancillary data contains simulation input file

Prediction of Helicopter Rotor Hover Performance using High Fidelity CFD Methods

No abstract available

The VOLNA code for the numerical modelling of tsunami waves: generation, propagation and inundation

A novel tool for tsunami wave modelling is presented. This tool has the potential of being used for operational purposes: indeed, the numerical code \VOLNA is able to handle the complete life-cycle of a tsunami (generation, propagation and run-up along the coast). The algorithm works on unstructured triangular meshes and thus can be run in arbitrary complex domains. This paper contains the detailed description of the finite volume scheme implemented in the code. The numerical treatment of the wet/dry transition is explained. This point is crucial for accurate run-up/run-down computations. Most existing tsunami codes use semi-empirical techniques at this stage, which are not always sufficient for tsunami hazard mitigation. Indeed the decision to evacuate inhabitants is based on inundation maps which are produced with this type of numerical tools. We present several realistic test cases that partially validate our algorithm. Comparisons with analytical solutions and experimental data are performed. Finally the main conclusions are outlined and the perspectives for future research presented.Comment: 47 pages, 27 figures. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Comparison of structured- and unstructured-grid, compressible and incompressible methods using the vortex pairing problem

The accuracy, robustness, dissipation characteristics and efficiency of several structured and unstructured grid methods are investigated with reference to the low Mach double vortex pairing flow problem. The aim of the study is to shed light into the numerical advantages and disadvantages of different numerical discretizations, principally designed for shock-capturing, in low Mach vortical flows. The methods include structured and unstructured finite volume and Lagrange-Remap methods, with accuracy ranging from 2nd to 9th-order, with and without applying low-Mach corrections. Comparison of the schemes is presented for the vortex evolution, momentum thickness, as well as for their numerical dissipation versus the viscous and total dissipation. The study shows that the momentum thickness and large scale features of a basic vortical structure are well resolved even at the lowest grid resolution of 32×32 provided that the numerical schemes are of a high-order of accuracy or the numerical framework is sufficiently non-dissipative. The implementation of the finite volume methods in unstructured triangular meshes provides the best results even without low Mach number corrections provided that a higher-order advective discretization for the advective fluxes is employed. The compressible Lagrange-Remap framework is computationally the fastest one, although the numerical error for the momentum thickness does not reduce as fast as for other numerical schemes and computational frameworks, e.g., when higher-order schemes are utilized. It is also shown that the low-Mach number correction has a lesser effect on the results as the order of the spatial accuracy increases