Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes

DOI10.1016/j.jcp.2019.109137zbMath1453.76112OpenAlexW2990794724MaRDI QIDQ2223036

F. E. Uilhoorn

Publication date: 28 January 2021

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2019.109137

zbMATH Keywords

Riemann problemsmethod of manufactured solutionshydraulic shocknonconservative schemeweighted essentially nonoscillatory

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Finite volume methods applied to problems in fluid mechanics (76M12) Gas dynamics (general theory) (76N15) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Uses Software

• HE-E1GODF
• PVM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite volume schemes for dispersive wave propagation and runup
• A high order moving boundary treatment for compressible inviscid flows
• A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems
• On high order strong stability preserving Runge-Kutta and multi step time discretizations
• FORCE schemes on unstructured meshes. II: Non-conservative hyperbolic systems
• On postshock oscillations due to shock capturing schemes in unsteady flows
• Uniformly high order accurate essentially non-oscillatory schemes. III. (Reprint)
• Transient flow in natural gas pipeline - the effect of pipeline thermal model
• ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows
• High resolution schemes for hyperbolic conservation laws
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Approximate solution of ordinary differential equations and their systems through discrete and continuous embedded Runge-Kutta formulae and upgrading of their order
• Weighted essentially non-oscillatory schemes
• Upwind methods for hyperbolic conservation laws with source terms
• A well-behaved TVD limiter for high-resolution calculations of unsteady flow
• Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
• Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
• Definition and weak stability of nonconservative products
• Efficient implementation of weighted ENO schemes
• Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws
• An explicit staggered-grid method for numerical simulation of large-scale natural gas pipeline networks
• A review on TVD schemes and a refined flux-limiter for steady-state calculations
• A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems
• Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations
• On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas
• An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
• A steady-state capturing method for hyperbolic systems with geometrical source terms
• A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport
• Relation between PVM schemes and simple Riemann solvers
• A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods
• High Resolution Schemes and the Entropy Condition
• On some fast well-balanced first order solvers for nonconservative systems
• Godunov method for nonconservative hyperbolic systems
• Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws
• Riemann Solvers and Numerical Methods for Fluid Dynamics
• Total-Variation-Diminishing Time Discretizations
• Why Nonconservative Schemes Converge to Wrong Solutions: Error Analysis
• A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations
• High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems
• Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
• On Runge-Kutta processes of high order

This page was built for publication: Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes