Maximum-principle-preserving, steady-state-preserving and large time-stepping high-order schemes for scalar hyperbolic equations with source terms

DOI10.4208/cicp.oa-2023-0143zbMATH Open1536.65084MaRDI QIDQ6537081

Songhe Song, Hong Zhang, Lele Liu, Xu Qian

Publication date: 14 May 2024

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

zbMATH Keywords

hyperbolic equationsweighted compact nonlinear schemesmaximum-principle-preservingparametric relaxation Runge-Kutta schemessteady-state-preserving

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Cites Work

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• A parametrized maximum principle preserving flux limiter for finite difference RK-WENO schemes with applications in incompressible flows
• On high order strong stability preserving Runge-Kutta and multi step time discretizations
• High order strong stability preserving time discretizations
• Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
• A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws
• Effects of difference scheme type in high-order weighted compact nonlinear schemes
• High resolution schemes for hyperbolic conservation laws
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Contractivity of Runge-Kutta methods
• Weighted essentially non-oscillatory schemes
• High-order accurate dissipative weighted compact nonlinear schemes.
• Two barriers on strong-stability-preserving time discretization methods
• Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms
• Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
• Contractivity in the numerical solution of initial value problems
• Efficient implementation of weighted ENO schemes
• On the stability and accuracy of partially and fully implicit schemes for phase field modeling
• Robust explicit formulation of weighted compact nonlinear scheme
• High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws
• Explicit third-order unconditionally structure-preserving schemes for conservative Allen-Cahn equations
• Maximum-principle-preserving local discontinuous Galerkin methods for Allen-Cahn equations
• High order sign-preserving and well-balanced exponential Runge-Kutta discontinuous Galerkin methods for the shallow water equations with friction
• Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations
• Quenching study of two-dimensional fractional reaction-diffusion equation from combustion process
• Third-order conservative sign-preserving and steady-state-preserving time integrations and applications in stiff multispecies and multireaction detonations
• Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws
• An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
• Parametrized positivity preserving flux limiters for the high order finite difference WENO scheme solving compressible Euler equations
• High-order bound-preserving discontinuous Galerkin methods for multicomponent chemically reacting flows
• Strong stability-preserving high-order time discretization methods
• Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term
• Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
• Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem
• High Resolution Schemes and the Entropy Condition
• Riemann Solvers, the Entropy Condition, and Difference
• Total-Variation-Diminishing Time Discretizations
• Finite Difference WENO Schemes with Lax--Wendroff-Type Time Discretizations
• High-Order Bound-Preserving Discontinuous Galerkin Methods for Stiff Multispecies Detonation
• Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
• A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
• Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes
• A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations
• High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes
• Moment-Based Multi-Resolution HWENO Scheme for Hyperbolic Conservation Laws
• Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
• Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models
• Developing high-order weighted compact nonlinear schemes
• A family of structure-preserving exponential time differencing Runge-Kutta schemes for the viscous Cahn-Hilliard equation

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