$$H$$ -adaptive Mesh Method with Double Tolerance Adaptive Strategy for Hyperbolic Conservation Laws

2013 ◽  
Vol 56 (3) ◽  
pp. 616-636 ◽  
Author(s):  
Ruo Li ◽  
Shuonan Wu
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Adaptive Mesh ◽  
Adaptive Strategy ◽  
Hyperbolic Conservation ◽  
Adaptive Mesh Method ◽  
Mesh Method

ENTROPY CONSERVATIVE SCHEMES AND ADAPTIVE MESH SELECTION FOR HYPERBOLIC CONSERVATION LAWS

2010 ◽  
Vol 07 (03) ◽  
pp. 383-404 ◽  
Author(s):  
CHRISTOS ARVANITIS ◽  
CHARALAMBOS MAKRIDAKIS ◽  
NIKOLAOS I. SFAKIANAKIS
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Adaptive Mesh ◽  
Mesh Adaptivity ◽  
Hyperbolic Conservation ◽  
Fully Discrete ◽  
Conservative Schemes ◽  
Mesh Selection ◽  
Adaptive Schemes ◽  
Selection For

We consider numerical schemes which combine non-uniform, adaptively redefined spatial meshes with entropy conservative schemes for the evolution step for shock computations. We observe that the resulting adaptive schemes yield approximations free of oscillations in contrast to known fully discrete entropy conservative schemes on uniform meshes. We conclude that entropy conservative schemes are transformed to entropy diminishing schemes when combined with the proposed geometrically driven mesh adaptivity.

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