On the stability and accuracy of the spectral difference method

From MaRDI portal

Publication:618412

Jump to:navigation, search

DOI10.1007/s10915-008-9201-0zbMath1203.65132OpenAlexW1983014318MaRDI QIDQ618412

Kris Van Den Abeele, Chris Lacor, Zhi Jian Wang

Publication date: 16 January 2011

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-008-9201-0

zbMATH Keywords

stability spectral difference method wave propagation properties

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items

Flux reconstruction using Jacobi correction functions in discontinuous spectral element method, Strong compact formalism for characteristic boundary conditions with discontinuous spectral methods, Numerical simulation for unsteady compressible micropolar fluid flow, An arbitrary high-order spectral difference method for the induction equation, A comparative study from spectral analyses of high-order methods with non-constant advection velocities, A high-order compact limiter based on spatially weighted projections for the spectral volume and the spectral differences method, A stable spectral difference approach for computations with triangular and hybrid grids up to the \(6^{th}\) order of accuracy, Computation of flows with shocks using the spectral difference method with artificial viscosity. I: Basic formulation and application, A study on the numerical dissipation of the spectral difference method for freely decaying and wall-bounded turbulence, The discontinuous Galerkin spectral element methods for compressible flows on two-dimensional mixed grids, Analysis of the dissipation and dispersion properties of the multi-domain Chebyshev pseudospectral method, On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods, Adjoint-based error estimation and mesh adaptation for the correction procedure via reconstruction method, A Divergence-Free High-Order Spectral Difference Method with Constrained Transport for Ideal Compressible Magnetohydrodynamics, A high-order spectral difference method for unstructured dynamic grids, A \(p\)-multigrid spectral difference method for two-dimensional unsteady incompressible Navier-Stokes equations, Absorbing boundary conditions for the Euler and Navier-Stokes equations with the spectral difference method, Application of modal filtering to a spectral difference method, A proof of the stability of the spectral difference method for all orders of accuracy, Fully-discrete spatial eigenanalysis of discontinuous spectral element methods: insights into well-resolved and under-resolved vortical flows, High-Order Spectral Difference Gas-Kinetic Schemes for Euler and Navier-Stokes Equations, A direct flux reconstruction scheme for advection-diffusion problems on triangular grids, An extended range of energy stable flux reconstruction methods on triangles, Revisiting the spectral analysis for high-order spectral discontinuous methods, A stable high-order spectral difference method for hyperbolic conservation laws on triangular elements, A stable interface element scheme for the \(p\)-adaptive lifting collocation penalty formulation, Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness, A new class of high-order energy stable flux reconstruction schemes for triangular elements, An optimized spectral difference scheme for CAA problems, Upwind Hybrid Spectral Difference Methods for Steady-State Navier–Stokes Equations, High-order accurate simulations of unsteady flow past plunging and pitching airfoils, Spatial eigenanalysis of spectral/\textit{hp} continuous Galerkin schemes and their stabilisation via DG-mimicking spectral vanishing viscosity for high Reynolds number flows, A \(P_N P_M-CPR \) framework for hyperbolic conservation laws, A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes, A fifth-order nonlinear spectral difference scheme for hyperbolic conservation laws, A conservative multirate explicit time integration method for computation of compressible flows, On the Spectral Difference Method with Modal Filtering Applied to the Euler Equations, A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations, A comparison of the discontinuous-Galerkin- and spectral-difference-method on triangulations using PKD polynomials, A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes, Large Eddy Simulation of a Muffler with the High-Order Spectral Difference Method, An implicit high-order spectral difference approach for large eddy simulation, Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES, A spectral-element dynamic model for the large-eddy simulation of turbulent flows, A new spectral difference method using hierarchical polynomial bases for hyperbolic conservation laws, Eigensolution analysis of spectral/\(hp\) continuous Galerkin approximations to advection-diffusion problems: insights into spectral vanishing viscosity, A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids, Spectral difference method for compressible flow on unstructured grids with mixed elements, Fourier analysis and evaluation of DG, FD and compact difference methods for conservation laws, Eigenanalysis and non-modal analysis of collocated discontinuous Galerkin discretizations with the summation-by-parts property, VALIDATION AND APPLICATION OF AN HIGH-ORDER SPECTRAL DIFFERENCE METHOD FOR FLOW INDUCED NOISE SIMULATION, A collocated-grid spectral difference method for compressible flows, An extended Discontinuous Galerkin and Spectral Difference Method with modal filtering, The spectral difference Raviart-Thomas method for two and three-dimensional elements and its connection with the flux reconstruction formulation, An improved fifth-order nonlinear spectral difference scheme for hyperbolic conservation laws, Stable spectral difference approach using Raviart-Thomas elements for 3D computations on tetrahedral grids

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:618412&oldid=12510806"