Topic
Roe solver
About: Roe solver is a research topic. Over the lifetime, 680 publications have been published within this topic receiving 48616 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.
8,689 citations
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
7,406 citations
Book•
1 Jan 2009
TL;DR: In this article, the authors present references and index Reference Record created on 2004-09-07, modified on 2016-08-08 and a reference record created on 2003-09 -07.
Abstract: Note: Includes references and index Reference Record created on 2004-09-07, modified on 2016-08-08
6,104 citations
Book•
27 Aug 1999
TL;DR: In this article, the generalized Riemann problem is used to solve the Euler Equation problem and the ADER approach is used for non-linear systems with finite forces in multiple dimensions.
Abstract: The Equations of Fluid Dynamics.- Notions on Hyperbolic Partial Differential Equations.- Some Properties of the Euler Equations.- The Riemann Problem for the Euler Equations.- Notions on Numerical Methods.- The Method of Godunov for Non#x2014 linear Systems.- Random Choice and Related Methods.- Flux Vector Splitting Methods.- Approximate#x2014 State Riemann Solvers.- The HLL and HLLC Riemann Solvers.- The Riemann Solver of Roe.- The Riemann Solver of Osher.- High#x2013 Order and TVD Methods for Scalar Equations.- High#x2013 Order and TVD Schemes for Non#x2013 Linear Systems.- Splitting Schemes for PDEs with Source Terms.- Methods for Multi#x2013 Dimensional PDEs.- Multidimensional Test Problems.- FORCE Fluxes in Multiple Space Dimensions.- The Generalized Riemann Problem.- The ADER Approach.- Concluding Remarks.
5,835 citations
TL;DR: This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes.
Abstract: This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes. Special attention is given to the Godunov-type schemes that result from using an approximate solution of the Riemann problem. For schemes based on flux splitting, the approximate Riemann solution can be interpreted as a solution of the collisionless Boltzmann equation.
3,584 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 2 |
| 2024 | 4 |
| 2023 | 13 |
| 2022 | 32 |
| 2021 | 7 |
| 2020 | 11 |