A new finite element formulation for computational fluid dynamics: II. Beyond SUPG
Computer Methods in Applied Mechanics and Engineering
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Convergence of spectral methods for nonlinear conservation laws
SIAM Journal on Numerical Analysis
Shock capturing by the spectral viscosity method
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
The behavior of flux difference splitting schemes near slowly moving shock waves
Journal of Computational Physics
High order filtering methods for approximating hyperbolic systems of conservation laws
Journal of Computational Physics
Legendre pseudospectral viscosity method for nonlinear conservation laws
SIAM Journal on Numerical Analysis
The effects of numerical viscosities. I: slowly moving shocks
Journal of Computational Physics
Computations of slowly moving shocks
Journal of Computational Physics
Low-dissipative high-order shock-capturing methods using characteristic-based filters
Journal of Computational Physics
On the use of shock-capturing schemes for large-eddy simulation
Journal of Computational Physics
Journal of Computational Physics
A spectral vanishing viscosity method for large-eddy simulations
Journal of Computational Physics
On the application of congruent upwind discretizations for large eddy simulations
Journal of Computational Physics
Implicit subgrid-scale modeling by adaptive deconvolution
Journal of Computational Physics
Short Note: Hyperviscosity for shock-turbulence interactions
Journal of Computational Physics
Spectral Vanishing Viscosity Method for Large-Eddy Simulation of Turbulent Flows
Journal of Scientific Computing
An artificial nonlinear diffusivity method for supersonic reacting flows with shocks
Journal of Computational Physics
A stabilized semi-implicit Galerkin scheme for Navier-Stokes equations
Journal of Computational and Applied Mathematics
From Suitable Weak Solutions to Entropy Viscosity
Journal of Scientific Computing
Dimension reduction method for ODE fluid models
Journal of Computational Physics
Increasing Accuracy and Efficiency for Regularized Navier-Stokes Equations
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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We develop a method for the modeling of flow discontinuities which can arise as weak solutions of inviscid conservation laws. Due to its similarity with recently proposed approximate deconvolution models for large-eddy simulation, the method potentially allows for a unified treatment of flow discontinuities and turbulent subgrid scales. A filtering approach is employed since for the filtered evolution equations the solution is smooth and can be solved for by standard central finite-difference schemes without special consideration of discontinuities. A sufficiently accurate representation of the filtered nonlinear combination of discontinuous solution components which arise from the convection term can be obtained by a regularized deconvolution applied to the filtered solution. For stable integration the evolution equations are supplemented by a relaxation regularization based on a secondary filter operation and a relaxation parameter. An estimate for the relaxation parameter is provided. The method is related to the spectral vanishing-viscosity method and the regularized Chapman-Enskog expansion method for conservation laws. We detail the approach and demonstrate its efficiency with the inviscid and viscous Burgers equations, the isothermal shock problem, and the one-dimensional Euler equations.