A class of robust numerical schemes to compute front propagation
| Autor: | Nicolas Therme |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN) |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Mathematical optimization MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics 01 natural sciences Stability (probability) Hamilton–Jacobi equation law.invention Maximum principle law Convergence (routing) Applied mathematics Polygon mesh Cartesian coordinate system 0101 mathematics Mathematics Numerical Analysis Finite volume method 010102 general mathematics Computational Mathematics Modeling and Simulation Scheme (mathematics) Hamilton-Jacobi Finite volume MUSL Convergence Stability [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | The SMAI journal of computational mathematics. 4:375-397 |
| ISSN: | 2426-8399 |
| DOI: | 10.5802/smai-jcm.39 |
| Popis: | In this work a class of finite volume schemes is proposed to numerically solve equations involving propagating fronts. They fall into the class of Hamilton-Jacobi equations. Finite volume schemes based on staggered grids, and initially developed to compute fluid flows, are adapted to the G-equation, using the Hamilton-Jacobi theoretical framework. The designed scheme has a maximum principle property and is consistent an monotonous on Cartesian grids. A convergence property is then obtained for the scheme on Cartesian grids and numerical experiments evidence the convergence of the scheme on more general meshes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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