Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow

DOI10.1016/j.jcp.2010.04.037zbMath1391.76489OpenAlexW2015892502MaRDI QIDQ630307

Chi-Wang Shu, Jing-Mei Qiu

Publication date: 17 March 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2010.04.037

zbMATH Keywords

semi-Lagrangian methodsWENO reconstructionconservative schemeadvection in incompressible flow

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)

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Uses Software

• Vador

Cites Work

• Unnamed Item
• High order strong stability preserving time discretizations
• Comparison of Eulerian Vlasov solvers
• The piecewise parabolic method (PPM) for gas-dynamical simulations
• A conservative high order semi-Lagrangian WENO method for the Vlasov equation
• On maximum-principle-satisfying high order schemes for scalar conservation laws
• Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic- type equations
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Advanced numerical approximation of nonlinear hyperbolic equations. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C. I. M. E.) held in Cetraro, Italy, June 23--28, 1997
• The semi-Lagrangian method for the numerical resolution of the Vlasov equation
• A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow
• Weighted essentially non-oscillatory schemes
• Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space
• A high-order discontinuous Galerkin method for 2D incompressible flows
• A second-order projection method for the incompressible Navier-Stokes equations
• Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov-Maxwell system.
• Efficient implementation of weighted ENO schemes
• Conservative semi-Lagrangian schemes for Vlasov equations
• Characteristic Galerkin Methods for Scalar Conservation Laws in One Dimension
• Nonoscillatory Interpolation Methods Applied to Vlasov-Based Models
• Hermite Spline Interpolation on Patches for Parallelly Solving the Vlasov-Poisson Equation
• High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
• High-Resolution Conservative Algorithms for Advection in Incompressible Flow
• A characteristic Galerkin method for discrete Boltzmann equation
• Conservative numerical schemes for the Vlasov equation
• A technique of treating negative weights in WENO schemes

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