Discontinuous Galerkin Method

Dolejší, Vít; Feistauer, Miloslav

doi:10.1007/978-3-319-19267-3

Cited by 127 publications

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“…We assume that there exists h 0 > 0 such that {T h } h∈(0,h0) is a system of triangulations which is shape-regular and locally quasi-uniform, see e.g. [9]. We do not require the conforming properties known from finite element methods.…”

Section: Problem Descriptionmentioning

confidence: 99%

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Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems

Dolejší

Roskovec

2017

Appl.Math.

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Section: Problem Descriptionmentioning

confidence: 99%

“…We discretize the equation (2.2) using the interior penalty Galerkin method (IPG), see e.g. [9], Section 4.6 or [19]. For u, ϕ ∈ H 2 (Ω, T h ) we define the forms…”

Section: Problem Descriptionmentioning

confidence: 99%

Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems

Dolejší

Roskovec

2017

Appl.Math.

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“…In order to overcome this difficulty we employ artificial viscosity forms, see [8]. They are based on the discontinuity indicator…”

Section: Space Discretization Of the Flow Problemmentioning

confidence: 99%

Finite volume - space-time discontinuous Galerkin method for the numerical simulation of compressible turbulent flow in time dependent domains

Česenek

2017

EPJ Web Conf.

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Abstract. The article is concerned with the numerical simulation of the compressible turbulent flow in time dependent domains. The mathematical model of flow is represented by the system of non-stationary ReynoldsAveraged Navier-Stokes (RANS) equations. The motion of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the RANS equations. This RANS system is equipped with two-equation k − ω turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k − ω turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.

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“…In order to overcome this difficulty we employ artificial viscosity form, see [7]. They are based on the discontinuity indicator…”

Section: Space Discretizationmentioning

confidence: 99%

Finite volume - space-time discontinuous Galerkin method for the solution of compressible turbulent flow

Česenek

2016

EPJ Web of Conferences

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Abstract. In this article we deal with numerical simulation of the non-stationary compressible turbulent flow. Compressible turbulent flow is described by the Reynolds-Averaged Navier-Stokes (RANS) equations. This RANS system is equipped with two-equation k-omega turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k-omega turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.

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Discontinuous Galerkin Method

Cited by 127 publications

References 0 publications

Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems

Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems

Finite volume - space-time discontinuous Galerkin method for the numerical simulation of compressible turbulent flow in time dependent domains

Finite volume - space-time discontinuous Galerkin method for the solution of compressible turbulent flow

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