Simulation of compressible viscous flow in time-dependent domains

Esenek, Jan; Feistauer, Miloslav; Horáček, Jaromı́r; Kučera, Václav; Prokopová, Jaroslava

doi:10.1016/j.amc.2011.08.077

Cited by 36 publications

(32 citation statements)

References 13 publications

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“…The procedures that have been adopted to overcome this difficulty can be roughly divided in two classes. From one side, it is possible to introduce additional numerical dissipation, either in the form of artificial viscosity (R. Hartmann & P.Houston 2002;Persson & Peraire 2006;Cesenek et al 2013), or by means of filtering (Radice & Rezzolla 2011). From another side, it is possible to isolate the so-called troubled cells, namely those affected by spurious oscillations, and adopt for them some sort of nonlinear finite-volume-type slope-limiting procedure (Cockburn & Shu 1998;J.Qiu & C-W.Shu 2004;Balsara et al 2007; J.…”

Section: Introductionmentioning

confidence: 99%

Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement

Zanotti

Fambri

Dumbser

2015

Mon. Not. R. Astron. Soc.

114

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We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allows for an arbitrary order of accuracy in both space and time, (ii) an a posteriori subcell finite volume limiter that is activated to avoid spurious oscillations at discontinuities without destroying the natural subcell resolution capabilities of the DG finite element framework and finally (iii) a space-time adaptive mesh refinement (AMR) framework with time-accurate local time-stepping.The divergence-free character of the magnetic field is instead taken into account through the so-called "divergence-cleaning" approach. The convergence of the new scheme is verified up to 5 th order in space and time and the results for a set of significant numerical tests including shock tube problems, the RMHD rotor and blast wave problems, as well as the Orszag-Tang vortex system are shown. We also consider a simple case of the relativistic Kelvin-Helmholtz instability with a magnetic field, emphasizing the potential of the new method for studying turbulent RMHD flows. We discuss the advantages of our new approach when the equations of relativistic MHD need to be solved with high accuracy within various astrophysical systems.

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Section: Introductionmentioning

confidence: 99%

Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement

Zanotti

Fambri

Dumbser

2015

Mon. Not. R. Astron. Soc.

114

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“…At most second order of accuracy in space and time is achieved by all the Lagrangian finite volume schemes mentioned so far. So-called direct ALE schemes, which do not need the remap phase because the numerical fluxes already take into account the final mesh velocity, are widely used in the context of fluid-structure interaction problems (FSI), see for example the high order ALE discontinuous Galerkin (DG) schemes presented in [17,31,43,44].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes

Boscheri

Dumbser

2015

J Sci Comput

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In this paper we present a new and efficient quadrature-free formulation for the family of cell-centered high order accurate direct arbitrary-Lagrangian-Eulerian one-step ADER-WENO finite volume schemes on unstructured triangular and tetrahedral meshes that has been developed by the authors in a recent series of papers (Boscheri et al. in J Comput ). High order of accuracy in time is obtained by using a local space-time Galerkin predictor on moving curved meshes, while a high order accurate nonlinear WENO method is adopted to produce high order essentially non-oscillatory reconstruction polynomials in space. The mesh is moved at each time step according to the solution of a node solver algorithm that assigns a unique velocity vector to each node of the mesh. A rezoning procedure can also be applied when mesh distortions and deformations become too severe. The space-time mesh is then constructed by straight edges connecting the vertex positions at the old time level t n with the new ones at the next time level t n+1 , yielding closed space-time control volumes, on the boundary of which the numerical flux must be integrated. This is done here with a new and efficient quadrature-free approach: the space-time boundaries are split into simplex sub-elements, i.e. either triangles in 2D or tetrahedra in 3D. This leads to space-time normal vectors as well as Jacobian matrices that are constant within each sub-element. Within the space-time Galerkin predictor stage that solves the Cauchy problem inside each element in the small, the discrete solution and the flux tensor are approximated using a nodal space-time basis. Since these space-time basis functions are defined on a reference element and do not change, their integrals over the simplex sub-surfaces of the space-time reference control volume can be integrated once and for all analytically during a preprocessing step. The resulting integrals are then used together B M. Dumbser 123 J Sci Comput with the space-time degrees of freedom of the predictor in order to compute the numerical flux that is needed in the finite volume scheme. We apply the high order algorithm presented in this paper to the equations of hydrodynamics obtaining convergence rates up to fourth order of accuracy in space and time. A set of classical Lagrangian test problems has been solved and the results have been compared with the ones given by the original formulation of the algorithm (Boscheri and Dumbser 2013, 2014). The efficiency has been monitored and measured for each test case and the new quadrature-free schemes were up to 3.7 times faster than the ones based on Gaussian quadrature.Keywords Arbitrary-Lagrangian-Eulerian (ALE) · Finite volume schemes · Quadraturefree flux integration · WENO reconstruction on moving unstructured meshes · High order of accuracy in space and time · Local rezoning · Hydrodynamics

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“…Our choice of the domain was motivated by number of works on fluid-structure interaction problems for vocal folds, e.g. [6], [2] and [8].…”

Section: Introductionmentioning

confidence: 99%

Incompressible and Compressible Viscous Flow With Low Mach Numbers

Balázsová¹,

Feistauer²,

Sváček³

et al. 2017

Topical Problems of Fluid Mechanics 2017

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In this paper we compare incompressible flow and low Mach number compressible viscous flow. Incompressible Navier-Stokes equations were solved by the classical finite element method and compressible Navier-Stokes equations were treated with the aid of discontinuous Galerkin method in space and backward difference method in time. We present numerical results for a flow in a channel which represents a simplified model of the human vocal tract. Presented numerical results give a good correspondence between the the incompressible flow and the compressible flow with low Mach numbers.

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Simulation of compressible viscous flow in time-dependent domains

Cited by 36 publications

References 13 publications

Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement

Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement

An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes

Incompressible and Compressible Viscous Flow With Low Mach Numbers

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