A 2D/3D Discrete Duality Finite Volume Scheme. Application to ECG simulation
نویسندگان
چکیده
This paper presents a 2D/3D discrete duality finite volume method for solving heterogeneous and anisotropic elliptic equations on very general unstructured meshes. The scheme is based on the definition of discrete divergence and gradient operators that fulfill a duality property mimicking the Green formula. As a consequence, the discrete problem is proved to be well-posed, symmetric and positive-definite. Standard numerical tests are performed in 2D and 3D and the results are discussed and compared with P1 finite elements ones. At last, the method is used for the resolution of a problem arising in biomathematics: the electrocardiogram simulation on a 2D mesh obtained from segmented medical images.
منابع مشابه
A 3D Discrete Duality Finite Volume Method for Nonlinear Elliptic Equations
Discrete Duality Finite Volume (DDFV) schemes have recently been developed in 2D to approximate nonlinear diffusion problems on general meshes. In this paper, a 3D extension of these schemes is proposed. The construction of this extension is detailed and its main properties are proved: a priori bounds, well-posedness and error estimates. The practical implementation of this scheme is easy. Nume...
متن کاملBenchmark 3D: a version of the DDFV scheme with cell/vertex unknowns on general meshes
This paper gives numerical results for a 3D extension of the 2D DDFV scheme. Our scheme is of the same inspiration as the one called CeVe-DDFV ([9]), with a more straightforward dual mesh construction. We sketch the construction in which, starting from a given 3D mesh (which can be non conformal and have arbitrary polygonal faces), one defines a dual mesh and a diamond mesh, reconstructs a disc...
متن کاملViscous Models Comparison in Water Impact of Twin 2D Falling Wedges Simulation by Different Numerical Solvers
In this paper, symmetric water entry of twin wedges is investigated for deadrise angle of 30 degree. Three numerical simulation of a symmetric impact, considering rigid body dynamic equations of motion in two-phase flow is presented. The two-phase flow around the wedges is solved by Finite Element based on Finite Volume method (FEM-FVM) which is used in conjunction with Volume of Fluid (VOF) sc...
متن کاملA hybrid scheme of single relaxation time lattice Boltzmann and finite volume methods coupled with discrete ordinates method for combined natural convection and volumetric radiation in an enclosure
This paper is focused on the application of hybrid Single relaxation time lattice Boltzmann and finite volume methods in conjunction with discrete ordinates method to simulate coupled natural convection and volumetric radiation in differentially heated enclosure, filled with an absorbing, emitting and non-scattering gray medium. In this work, the velocity and temperature fields are calculated u...
متن کاملOn 3D DDFV Discretization of Gradient and Divergence Operators: Discrete Functional Analysis Tools and Applications to Degenerate Parabolic Problems
We present a detailed survey of discrete functional analysis tools (consistency results, Poincaré and Sobolev embedding inequalities, discreteW 1,p compactness, discrete compactness in space and in time) for the so-called Discrete Duality (DDFV) Finite Volume schemes in three space dimensions. We concentrate mainly on the 3D CeVe-DDFV scheme presented in [3]. Some of our results are new, such a...
متن کامل