This paper presents a convergence analysis of the multi point flux approximation control volume method, MPFA, in two space dimensions. The MPFA version discussed here is the so–called O–method on general quadrilateral grids. The discretization is based on local mappings onto a reference square. The key ingredient in the analysis is an equivalence between the MPFA method and a mixed finite eleme...

The analysis of the Multi Point Flux Approximation (MPFA) method has so far relied on the possibility of seeing it as a mixed finite element method for which the convergence is then established. This type of analysis has been successfully applied to triangles and quadrilaterals, also in the case of rough meshes. The MPFA method has however much in common with another well known conservative met...

Subsurface formations that arise in the simulation of gas-injection processes for enhanced oil recovery may exhibit geometrically complex features with complicated large-scale connectivity. They must be included in simulations of flow and transport because they can fundamentally impact simulation results. However, to reduce computational costs, simulations are generally performed on grids that ...

We propose a new single-phase local transmissibility upscaling method for adapted grids in 3D domains that uses spatially varying and compact multi-point flux approximations (MPFA), based on the VCMP method previously introduced for 2-D Cartesian grids. For each cell face in the coarse upscaled grid, we create a local fine grid region surrounding the face on which we solve three generic local f...

In this paper, the cell-centered finite volume method (CC-FVM) has been presented to simulate the axisymmetric radial flow toward a pumping well. The model is applied to the unstructured triangular grids which allows to simulate inhomogeneous and complex-shaped domains. Due to the non-orthogonality of the irregular grids, the multipoint flux approximation (MPFA) methods are used to discretize t...

This paper investigates different variants of the multipoint flux approximation (MPFA) O-method in 2D, which rely on a transformation to an orthogonal reference space. This approach yields a system of equations with a symmetric matrix of coefficients. Different methods appear, depending on where the transformed permeability is evaluated. Midpoint and corner-point Wheeler was partially supported...

Individual robots are not effective at exploring large unmapped areas. An alternate approach is to use a swarm of simple robots that work together, rather than a single highly capable robot. The central-place foraging algorithm (CPFA) is effective for coordinating robot swarm search and collection tasks. Robots start at a centrally placed location (nest), explore potential targets in the area w...

Multipoint flux approximation (MPFA) techniques are commonly applied for discretizing the porous media flow equations within the context of finite volume numerical procedures. Although these methods can be applied to heterogeneous, anisotropic systems on generally unstructured grids, the inverse of the resulting linear operator can suffer from a loss of monotonicity at high permeability anisotr...

Communication between neurones in the central nervous system depends on synaptic transmission. The efficacy of synapses is determined by pre- and postsynaptic factors that can be characterized using quantal parameters such as the probability of neurotransmitter release, number of release sites, and quantal size. Existing methods of estimating the quantal parameters based on multiple probability...