대한수학회논문집 (Communications of the Korean Mathematical Society)
- 제13권3호
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- Pages.655-681
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- 1998
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
ON THE NUMERICAL METHODS FOR DISCONTINUITIES AND INTERFACES
초록
Discontinuous solutions or interfaces are common in nature, for examples, shock waves or material interfaces. However, their numerical computation is difficult by the feature of discontinuities. In this paper, we summarize the numerical approaches for discontinuities and interfaces appearing mostly in the system of hyperbolic conservation laws, and explain various numerical methods for them. We explain two numerical approaches to handle discontinuities in the solution: shock capturing and shock tracking, and illustrate their underlying algorithms and mathematical problems. The front tracking method is explained in details and the level set method is outlined briefly. The several applications of front tracking are illustrated, and the research issues in this field are discussed.