Numerical simulation of two-dimensional and three-dimensional axisymmetric advection–diffusion systems with complex geometries using finite-volume methods

2010 ◽  
Vol 466 (2118) ◽  
pp. 1621-1643 ◽  
Author(s):  
J. M. A. Ashbourn ◽  
L. Geris ◽  
A. Gerisch ◽  
C. J. S. Young
Keyword(s):  
Finite Volume ◽  
Three Dimensional ◽  
Finite Volume Methods ◽  
Two Dimensional ◽  
Corner Singularities ◽  
Bone Fracture Healing ◽  
Curved Boundaries ◽  
Advection Diffusion ◽  
Diffusion Systems ◽  
Volume Method

A finite-volume method has been developed that can deal accurately with complicated, curved boundaries for both two-dimensional and three-dimensional axisymmetric advection–diffusion systems. The motivation behind this is threefold. Firstly, the ability to model the correct geometry of a situation yields more accurate results. Secondly, smooth geometries eliminate corner singularities in the calculation of, for example, mechanical variables and thirdly, different geometries can be tested for experimental applications. An example illustrating each of these is given: fluid carrying a dye and rotating in an annulus, bone fracture healing in mice, and using vessels of different geometry in an ultracentrifuge.

Logically rectangular finite volume methods with adaptive refinement on the sphere

2009 ◽  
Vol 367 (1907) ◽  
pp. 4483-4496 ◽  
Author(s):  
Marsha J. Berger ◽  
Donna A. Calhoun ◽  
Christiane Helzel ◽  
Randall J. LeVeque
Keyword(s):  
Finite Volume ◽  
Shallow Water Equations ◽  
Adaptive Mesh Refinement ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Finite Volume Methods ◽  
Adaptive Refinement ◽  
Two Dimensional ◽  
Equilibrium Solutions ◽  
Courant Number

The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the G eo C law software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.

scholarly journals Discontinuous finite volume element method of two-dimensional unsaturated soil water movement problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fan Chen ◽  
Zhixiao Xu
Keyword(s):  
Soil Water ◽  
Finite Volume ◽  
Unsaturated Soil ◽  
Water Movement ◽  
Optimal Error Estimate ◽  
Two Dimensional ◽  
Fully Discrete ◽  
Volume Method ◽  
Movement Problem ◽  
Soil Water Movement

AbstractIn this paper, a numerical approximation method for the two-dimensional unsaturated soil water movement problem is established by using the discontinuous finite volume method. We prove the optimal error estimate for the fully discrete format. Finally, the reliability of the method is verified by numerical experiments. This method is not only simple to calculate, but also stable and reliable.

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