On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems
From MaRDI portal
Publication:6142997
DOI10.4208/cicp.oa-2022-0243OpenAlexW4387393797MaRDI QIDQ6142997
Publication date: 4 January 2024
Published in: Communications in Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4208/cicp.oa-2022-0243
Riemann problemRunge-Kutta methodWENO reconstructionshock-capturing methodsartificial viscosity approachHancock-Rodionov methodShu-Osher test problem
Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)
Cites Work
- Unnamed Item
- Unnamed Item
- Application of the principle of minimizing the derivative to the construction of finite-difference schemes for computing discontinuous solutions of gas dynamics. (Reprint)
- A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov
- Fast sweeping methods for hyperbolic systems of conservation laws at steady state. II
- Propagation of error into regions of smoothness for non-linear approximations to hyperbolic equations
- High resolution schemes for hyperbolic conservation laws
- Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
- Towards the ultimate conservative difference scheme. IV: A new approach to numerical convection
- Restoration of the contact surface in the HLL-Riemann solver
- Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
- Convergence of finite-difference schemes behind a shock front.
- Artificial viscosity to cure the carbuncle phenomenon: the three-dimensional case
- On the construction of combined finite-difference schemes of high accuracy
- Artificial viscosity in Godunov-type schemes to cure the carbuncle phenomenon
- On the accuracy of the discontinuous Galerkin method in calculation of shock waves
- Interaction of a shock with a density disturbance via shock fitting
- Efficient implementation of weighted ENO schemes
- Simplified artificial viscosity approach for curing the shock instability
- A general framework for the evaluation of shock-capturing schemes
- Artificial viscosity to cure the shock instability in high-order Godunov-type schemes
- Elimination of First Order Errors in Shock Calculations
- On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist–Osher and Roe
- Methods of increasing the accuracy in Godunov's scheme
- Monotonic scheme of the second order of approximation for the continuous calculation of non-equilibrium flows
- The Convergence Rate of Finite Difference Schemes in the Presence of Shocks
- A Remark on Numerical Errors Downstream of Slightly Viscous Shocks
- Computational Considerations for the Simulation of Shock-Induced Sound
- Elimination of First Order Errors in Time Dependent Shock Calculations
- Finite Volume Methods for Hyperbolic Problems
- Analysis of First Order Errors in Shock Calculations in Two Space Dimensions
