A compact high order finite volume method for hyperbolic conservation laws on unstructured grids

2015 ◽  
Author(s):  
Qian Wang ◽  
Yu-Xin Ren ◽  
Wanai Li
Keyword(s):  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Hyperbolic Conservation Laws ◽  
Unstructured Grids ◽  
High Order ◽  
Hyperbolic Conservation ◽  
Volume Method

scholarly journals Finite volume method in curvilinear coordinates for hyperbolic conservation laws

2011 ◽  
Vol 32 ◽  
pp. 163-176 ◽  
Author(s):  
A. Bonnement ◽  
T. Fajraoui ◽  
H. Guillard ◽  
M. Martin ◽  
A. Mouton ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Hyperbolic Conservation Laws ◽  
Curvilinear Coordinates ◽  
Hyperbolic Conservation ◽  
Volume Method

scholarly journals A Slope Constrained 4th Order Multi-Moment Finite Volume Method with WENO Limiter

2015 ◽  
Vol 18 (4) ◽  
pp. 901-930 ◽  
Author(s):  
Ziyao Sun ◽  
Honghui Teng ◽  
Feng Xiao
Keyword(s):  
Conservation Laws ◽  
Finite Volume ◽  
Solution Structure ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Weno Reconstruction ◽  
Hyperbolic Conservation ◽  
Average Value ◽  
High Order Schemes ◽  
Volume Method

AbstractThis paper presents a new and better suited formulation to implement the limiting projection to high-order schemes that make use of high-order local reconstructions for hyperbolic conservation laws. The scheme, so-called MCV-WENO4 (multi-moment Constrained finite Volume with WENO limiter of 4th order) method, is an extension of the MCV method of Ii & Xiao (2009) by adding the 1st order derivative (gradient or slope) at the cell center as an additional constraint for the cell-wise local reconstruction. The gradient is computed from a limiting projection using the WENO (weighted essentially non-oscillatory) reconstruction that is built from the nodal values at 5 solution points within 3 neighboring cells. Different from other existing methods where only the cell-average value is used in the WENO reconstruction, the present method takes account of the solution structure within each mesh cell, and thus minimizes the stencil for reconstruction. The resulting scheme has 4th-order accuracy and is of significant advantage in algorithmic simplicity and computational efficiency. Numerical results of one and two dimensional benchmark tests for scalar and Euler conservation laws are shown to verify the accuracy and oscillation-less property of the scheme.

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