A positivity-preserving high order finite volume compact-WENO scheme for compressible Euler equations

[1]  P. Lax.  Weak solutions of nonlinear hyperbolic equations and their numerical computation , 1954 .

[2]  I. Bohachevsky,et al.  Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .

[3]  G. Sod.  A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws , 1978 .

[4]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[5]  ShuChi-Wang,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes, II , 1989 .

[6]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[7]  B. Perthame,et al.  Boltzmann type schemes for gas dynamics and the entropy property , 1990 .

[8]  P. Roe,et al.  On Godunov-type methods near low densities , 1991 .

[9]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[10]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .

[11]  Bernardo Cockburn,et al.  Nonlinearly stable compact schemes for shock calculations , 1994 .

[12]  Philippe Villedieu,et al.  High-Order Positivity-Preserving Kinetic Schemes for the Compressible Euler Equations , 1996 .

[13]  Nikolaus A. Adams,et al.  A High-Resolution Hybrid Compact-ENO Scheme for Shock-Turbulence Interaction Problems , 1996 .

[14]  Chi-Wang Shu,et al.  On positivity preserving finite volume schemes for Euler equations , 1996 .

[15]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[16]  Hiroshi Maekawa,et al.  Compact High-Order Accurate Nonlinear Schemes , 1997 .

[17]  Wang Chi-Shu,et al.  Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws , 1997 .

[18]  Derek M. Causon,et al.  On the Choice of Wavespeeds for the HLLC Riemann Solver , 1997, SIAM J. Sci. Comput..

[19]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[20]  Datta V. Gaitonde,et al.  Optimized Compact-Difference-Based Finite-Volume Schemes for Linear Wave Phenomena , 1997 .

[21]  Chi-Wang Shu.  Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws , 1998 .

[22]  K. Xu,et al.  Gas-kinetic schemes for the compressible Euler equations: Positivity-preserving analysis , 1999 .

[23]  Kun Xu,et al.  Gas-kinetic schemes for the compressible Euler equations : Positivity-preserving analysis , 1999 .

[24]  Jean-Marc Moschetta,et al.  Regular Article: Positivity of Flux Vector Splitting Schemes , 1999 .

[25]  Xiaogang Deng,et al.  Developing high-order weighted compact nonlinear schemes , 2000 .

[26]  Chi-Wang Shu,et al.  Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy , 2000 .

[27]  Li Jiang,et al.  Weighted Compact Scheme for Shock Capturing , 2001 .

[28]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[29]  Sergio Pirozzoli,et al.  Conservative Hybrid Compact-WENO Schemes for Shock-Turbulence Interaction , 2002 .

[30]  Yuxin Ren,et al.  A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws , 2003 .

[31]  M. Piller,et al.  Finite-volume compact schemes on staggered grids , 2004 .

[32]  Martine Baelmans,et al.  A finite volume formulation of compact central schemes on arbitrary structured grids , 2004 .

[33]  Raphaël Loubère,et al.  A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods , 2005 .

[34]  Zhi Gao,et al.  High-resolution finite compact difference schemes for hyperbolic conservation laws , 2006, J. Comput. Phys..

[35]  Wai-Sun Don,et al.  An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws , 2008, J. Comput. Phys..

[36]  Chi-Wang Shu,et al.  Development of nonlinear weighted compact schemes with increasingly higher order accuracy , 2008, J. Comput. Phys..

[37]  Marzio Piller,et al.  Compact finite volume schemes on boundary-fitted grids , 2008, J. Comput. Phys..

[38]  Chi-Wang Shu,et al.  High order conservative Lagrangian schemes with Lax-Wendroff type time discretization for the compressible Euler equations , 2009, J. Comput. Phys..

[39]  Chi-Wang Shu,et al.  High Order Strong Stability Preserving Time Discretizations , 2009, J. Sci. Comput..

[40]  Xiangxiong Zhang,et al.  On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes , 2010, J. Comput. Phys..

[41]  Xiangxiong Zhang,et al.  On maximum-principle-satisfying high order schemes for scalar conservation laws , 2010, J. Comput. Phys..

[42]  Xiangxiong Zhang,et al.  Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[43]  Xiangxiong Zhang,et al.  Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms , 2011, J. Comput. Phys..

[44]  Wai-Sun Don,et al.  High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws , 2011, J. Comput. Phys..

[45]  Dinshaw S. Balsara,et al.  Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics , 2012, J. Comput. Phys..

[46]  Xiangxiong Zhang,et al.  Positivity-preserving high order finite difference WENO schemes for compressible Euler equations , 2012, J. Comput. Phys..

[47]  Xiangxiong Zhang,et al.  Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes , 2011, Journal of Scientific Computing.

[48]  James D. Baeder,et al.  Compact Reconstruction Schemes with Weighted ENO Limiting for Hyperbolic Conservation Laws , 2012, SIAM J. Sci. Comput..

[49]  Chi-Wang Shu,et al.  Improvement of convergence to steady state solutions of Euler equations with weighted compact nonlinear schemes , 2013 .

[50]  Nikolaus A. Adams,et al.  Positivity-preserving method for high-order conservative schemes solving compressible Euler equations , 2013, J. Comput. Phys..

[51]  Chi-Wang Shu,et al.  A new class of central compact schemes with spectral-like resolution I: Linear schemes , 2013, J. Comput. Phys..

[52]  Chi-Wang Shu,et al.  Positivity-preserving Lagrangian scheme for multi-material compressible flow , 2014, J. Comput. Phys..

[53]  Zhengfu Xu,et al.  Parametrized Positivity Preserving Flux Limiters for the High Order Finite Difference WENO Scheme Solving Compressible Euler Equations , 2014, J. Sci. Comput..