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L 1 ‐type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton‐Jacobi equations
Author(s) -
Rathan Samala
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4855
Subject(s) - stencil , hamilton–jacobi equation , smoothness , mathematics , scheme (mathematics) , nonlinear system , type (biology) , norm (philosophy) , mathematical analysis , finite difference scheme , ecology , physics , computational science , quantum mechanics , political science , law , biology
Summary This article presents an improved fifth‐order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton‐Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L 1 ‐norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one‐ and two‐dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.