Name
Abstract | ||
|---|---|---|
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed solutions are evolved in time with a fourth-order accuracy by tracing the characteristics of the cubic polynomials. As a result, our temporal update scheme provides a significantly simpler and computationally more efficient approach in achieving fourth order accuracy in time, relative to the comparable fourth-order Runge–Kutta method. We demonstrate that the solutions of PCM converges at fifth-order in solving 1D smooth flows described by hyperbolic conservation laws. We test the new scheme on a range of numerical experiments, including both gas dynamics and magnetohydrodynamics applications in multiple spatial dimensions. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.jcp.2017.04.004 | Journal of Computational Physics |
Keywords | Field | DocType |
High-order methods,Piecewise cubic method,Finite volume method,Gas dynamics,Magnetohydrodynamics,Godunov's method | Mathematical optimization,Gas dynamics,Mathematical analysis,Cubic function,Magnetohydrodynamics,Computational fluid dynamics,Finite volume method,Piecewise,Tracing,Mathematics,Conservation law | Journal |
Volume | ISSN | Citations |
341 | 0021-9991 | 2 |
PageRank | References | Authors |
0.36 | 29 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dongwook Lee | 1 | 2 | 0.36 |
| Hugues Faller | 2 | 2 | 0.36 |
| Adam Reyes | 3 | 4 | 1.06 |