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
High accuracy solutions of incompressible Navier-Stokes equations
Journal of Computational Physics
A perturbational h4 exponential finite difference scheme for the convective diffusion equation
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
A level-set algorithm for tracking discontinuities in hyperbolic conservation laws
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
A Compact Fourth-Order Finite Difference Scheme for Unsteady Viscous Incompressible Flows
Journal of Scientific Computing
Resolution of high order WENO schemes for complicated flow structures
Journal of Computational Physics
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The upwind schemes play an important role in CFD. In this paper, some high order schemes are constructed without expanding the stencil and by modifying coefficients (MC) of the upwind schemes. According to our theoretical analysis, we show that MC approach preserves the desirable properties which the underlying schemes possess. We apply these new schemes to the linear scalar equation, Burgers equation and the hyperbolic system of conservation laws for simulating Rayleigh-Taylor instability, and show that MC approach increases the accurate order and improves efficiency in comparison with the underlying scheme.