Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection
Computer Methods in Applied Mechanics and Engineering
High-order ENO schemes applied to two- and three-dimensional compressible flow
Applied Numerical Mathematics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A well-behaved TVD limiter for high-resolution calculations of unsteady flow
Journal of Computational Physics
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A family of high order finite difference schemes with good spectral resolution
Journal of Computational Physics
Large-eddy simulation of the shock/turbulence interaction
Journal of Computational Physics
Journal of Computational Physics
ADER: Arbitrary High Order Godunov Approach
Journal of Scientific Computing
Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows
Journal of Computational Physics
An artificial nonlinear diffusivity method for supersonic reacting flows with shocks
Journal of Computational Physics
Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations
Journal of Computational Physics
A characteristic-based shock-capturing scheme for hyperbolic problems
Journal of Computational Physics
A high-order finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM)
Journal of Computational Physics
Asymptotic and numerical analysis of an inviscid bounded vortex flow at low Mach number
Journal of Computational Physics
Dissipative issue of high-order shock capturing schemes with non-convex equations of state
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
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This paper deals with the development of accurate one-step schemes for the numerical simulation of unsteady compressible flows. Pursuing our work in Daru and Tenaud [V. Daru, C. Tenaud, Comput. Fluids 30 (2001) 89] where third-order schemes were considered, we follow the Lax-Wendroff approach to develop high order TVD combined time-space schemes by correcting the successive modified equations. In the scalar case, TVD schemes accurate up to seventh order (OSTVD7) in time and space are obtained (in smooth regions and away from extrema). To avoid the clipping and the loss of accuracy that is common to the TVD schemes near extrema, we develop monotonicitypreserving (MP) conditions derived from Suresh and Huynh [A. Suresh, H.T. Huynh, J. Comput. Phys. 136 (1997) 83] to locally relax the TVD limitation for this family of one-step schemes. Numerical results for long time integration in the scalar case show that the MP one-step approach gives the best results compared to sever multistate schemes, including WENO schemes. The extension to systems and to the multidimensional case is done in a simplified way which does not preserve the scalar order of accuracy. However we show that the resulting schemes have a very low level of error. For validation, the present algorithm has been checked on several classical one-dimensional and multidimensional test cases, including both viscous and inviscid flows: a moving shock wave interacting with a sine wave, the Lax shock tube problem, the 2D inviscid double Mach reflection and the 2D viscous shock wave-vortex interaction. By computing these various test cases, we demonstrate that very accurate results can be obtained by using the one-step MP approach which is very competitive compared to multistage high order schemes.