## Relationships among some conservative discretization methods.(English)Zbl 1010.76064

Chen, Zhangxin (ed.) et al., Numerical treatment of multiphase flows in porous media. Proceedings of the international workshop, Beijing, China, August 2-6, 1999. Berlin: Springer. Lect. Notes Phys. 552, 267-282 (2000).
Summary: We discuss relationships among various mass-conservative discretization techniques for equations of the type $$-\nabla\cdot{\mathbf K}\nabla p=q$$ on distorted logically rectangular meshes. The case of heterogeneous anisotropic $${\mathbf K}$$ is important for applications to subsurface porous media, in particular to the groundwater flow equation and to the pressure equation of petroleum reservoir simulation. Some methods are based on $${\mathbf K}$$ itself, others on $${\mathbf K}^{-1}$$. Within one of these groups, mass lumping and quadrature can be keys to understanding connections between methods; incomplete inversion of the mass matrix is useful in relating one group to the other.
For the entire collection see [Zbl 0986.00070].

### MSC:

 76M12 Finite volume methods applied to problems in fluid mechanics 76S05 Flows in porous media; filtration; seepage 86A05 Hydrology, hydrography, oceanography