Application of modal filtering to a spectral difference method
From MaRDI portal
Publication:4586616
DOI10.1090/mcom/3257zbMath1376.65133arXiv1604.00929OpenAlexW2339742105MaRDI QIDQ4586616
Philipp Öffner, Thomas Sonar, Jan Glaubitz
Publication date: 30 October 2017
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.00929
stabilityorthogonal polynomialsnumerical exampleserror boundhyperbolic conservation lawshigh order methodsspectral difference methodmodal filtering
Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
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Cites Work
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- On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods
- Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations
- On the stability and accuracy of the spectral difference method
- A proof of the stability of the spectral difference method for all orders of accuracy
- A new class of high-order energy stable flux reconstruction schemes
- Insights from von Neumann analysis of high-order flux reconstruction schemes
- A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids
- Robust reprojection methods for the resolution of the Gibbs phenomenon
- Aliasing errors due to quadratic nonlinearities on triangular spectral /\(hp\) element discretisations
- Spectral methods on triangles and other domains
- Family of spectral filters for discontinuous problems
- High-order methods for computational fluid dynamics: a brief review of compact differential formulations on unstructured grids
- Artificial viscosity for correction procedure via reconstruction using summation-by-parts operators
- Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators
- A conservative staggered-grid Chebyshev multidomain method for compressible flows
- Summation-by-parts operators for correction procedure via reconstruction
- Spectral convergence for orthogonal polynomials on triangles
- On the connection between the spectral volume and the spectral difference method
- Spectral difference method for unstructured grids. I. Basic formulation
- Spectral difference method for unstructured grids. II. Extension to the Euler equations
- An extended Discontinuous Galerkin and Spectral Difference Method with modal filtering
- Detecting Edges in High Order Methods for Hyperbolic Conservation Laws
- Application of spectral filtering to discontinuous Galerkin methods on triangulations
- Filtering in Legendre spectral methods
- Convergence of Spectral Methods for Nonlinear Conservation Laws
- On the Gibbs Phenomenon and Its Resolution
- Chebyshev--Legendre Spectral Viscosity Method for Nonlinear Conservation Laws
- Legendre Pseudospectral Viscosity Method for Nonlinear Conservation Laws
- A Lobatto interpolation grid over the triangle
- Orthogonal Polynomials of Several Variables
- Spectral/hp Element Methods for Computational Fluid Dynamics
- Spectral methods for hyperbolic problems
