An Assessment of the Efficiency of Nodal Discontinuous Galerkin Spectral Element Methods

2013 ◽  
pp. 223-235 ◽  
Author(s):  
David A. Kopriva ◽  
Edwin Jimenez
Keyword(s):  
Discontinuous Galerkin ◽  
Spectral Element ◽  
Spectral Element Methods

scholarly journals Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods

2019 ◽  
Vol 81 (2) ◽  
pp. 820-844
Author(s):  
Marvin Bohm ◽  
Sven Schermeng ◽  
Andrew R. Winters ◽  
Gregor J. Gassner ◽  
Gustaaf B. Jacobs
Keyword(s):  
Discontinuous Galerkin ◽  
Spectral Element ◽  
High Order ◽  
Shock Capturing ◽  
Spectral Element Methods

scholarly journals Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps

2021 ◽  
Vol 88 (1) ◽  
Author(s):  
David A. Kopriva ◽  
Gregor J. Gassner ◽  
Jan Nordström
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Discontinuous Galerkin ◽  
Hyperbolic Equations ◽  
Spectral Element ◽  
Spectral Element Methods ◽  
Conservation Condition ◽  
Energy Bound ◽  
Dissipative Boundary ◽  
Linear Hyperbolic Equations

AbstractWe use the behavior of the $$L_{2}$$ L 2 norm of the solutions of linear hyperbolic equations with discontinuous coefficient matrices as a surrogate to infer stability of discontinuous Galerkin spectral element methods (DGSEM). Although the $$L_{2}$$ L 2 norm is not bounded in terms of the initial data for homogeneous and dissipative boundary conditions for such systems, the $$L_{2}$$ L 2 norm is easier to work with than a norm that discounts growth due to the discontinuities. We show that the DGSEM with an upwind numerical flux that satisfies the Rankine–Hugoniot (or conservation) condition has the same energy bound as the partial differential equation does in the $$L_{2}$$ L 2 norm, plus an added dissipation that depends on how much the approximate solution fails to satisfy the Rankine–Hugoniot jump.

Computation of Forward-Time Finite-Time Lyapunov Exponents Using Discontinuous-Galerkin Spectral Element Methods

2013 ◽  
Author(s):  
Daniel A. Nelson ◽  
Gustaaf B. Jacobs
Keyword(s):  
Lyapunov Exponents ◽  
Discontinuous Galerkin ◽  
Finite Time ◽  
Deformation Gradient ◽  
Spectral Element ◽  
High Order ◽  
Exact Equation ◽  
Spectral Element Methods ◽  
Finite Time Lyapunov Exponents ◽  
Flow Map

We present an algorithm for computing forward-time finite-time Lyapunov exponents (FTLEs) using discontinuous-Galerkin (DG) operators. Passive fluid tracers are initialized at Gauss-Lobatto quadrature nodes and advected concurrently with direct numerical simulation (DNS) using DG spectral element methods. The flow map is approximated by a high-order polynomial and the deformation gradient tensor is then determined by the spectral derivative. Since DG operators are used to compute the deformation gradient, the algorithm is high-order accurate and is consistent with the DG methods used to compute the fluid solution. The method is validated with a benchmark of a periodic gyre, a vortex advected in uniform flow and the flow around a square cylinder. An exact equation for the FTLE of the advected vortex is derived.

High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations

2014 ◽  
Vol 76 (8) ◽  
pp. 522-548 ◽  
Author(s):  
Andrea D. Beck ◽  
Thomas Bolemann ◽  
David Flad ◽  
Hannes Frank ◽  
Gregor J. Gassner ◽  
...  
Keyword(s):  
Turbulent Flow ◽  
Discontinuous Galerkin ◽  
Spectral Element ◽  
High Order ◽  
Spectral Element Methods ◽  
Flow Simulations
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