High-order least-square-based finite-difference–finite-volume method for simulation of incompressible thermal flows on arbitrary grids

2019 ◽  
Vol 100 (6) ◽  
Author(s):  
Y. Y. Liu ◽  
H. W. Zhang ◽  
L. M. Yang ◽  
C. Shu
Keyword(s):  
Finite Difference ◽  
Finite Volume Method ◽  
Finite Volume ◽  
High Order ◽  
Least Square ◽  
Volume Method ◽  
Thermal Flows

scholarly journals Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

2015 ◽  
Vol 17 (2) ◽  
pp. 337-370 ◽  
Author(s):  
Ossian O'Reilly ◽  
Jan Nordström ◽  
Jeremy E. Kozdon ◽  
Eric M. Dunham
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Difference Method ◽  
High Order ◽  
Complex Geometries ◽  
Earthquake Rupture ◽  
Volume Method ◽  
High Order Finite Difference

AbstractWe couple a node-centered finite volume method to a high order finite difference method to simulate dynamic earthquake ruptures along nonplanar faults in two dimensions. The finite volume method is implemented on an unstructured mesh, providing the ability to handle complex geometries. The geometric complexities are limited to a small portion of the overall domain and elsewhere the high order finite difference method is used, enhancing efficiency. Both the finite volume and finite difference methods are in summation-by-parts form. Interface conditions coupling the numerical solution across physical interfaces like faults, and computational ones between structured and unstructured meshes, are enforced weakly using the simultaneous-approximation-term technique. The fault interface condition, or friction law, provides a nonlinear relation between fields on the two sides of the fault, and allows for the particle velocity field to be discontinuous across it. Stability is proved by deriving energy estimates; stability, accuracy, and efficiency of the hybrid method are confirmed with several computational experiments. The capabilities of the method are demonstrated by simulating an earthquake rupture propagating along the margins of a volcanic plug.

scholarly journals Pixels and their neighbors: Finite volume

2016 ◽  
Vol 35 (8) ◽  
pp. 703-706 ◽  
Author(s):  
Rowan Cockett ◽  
Lindsey J. Heagy ◽  
Douglas W. Oldenburg
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Direct Current ◽  
Numerical Results ◽  
Dc Resistivity ◽  
Matrix Representations ◽  
Volume Method

We take you on the journey from continuous equations to their discrete matrix representations using the finite-volume method for the direct current (DC) resistivity problem. These techniques are widely applicable across geophysical simulation types and have their parallels in finite element and finite difference. We show derivations visually, as you would on a whiteboard, and have provided an accompanying notebook at http://github.com/seg to explore the numerical results using SimPEG ( Cockett et al., 2015 ).

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