mixed convection of al 2 o 3 -water nanofluid in a square microcavity is investigated numerically. governing equations are discretized and solved using the finite volume method and simpler algorithm. the knudsen number is selected between 0.001 and 0.1 to consider slip velocity and the jump temperature boundary conditions. results showed that nusselt number is a function of richardson number, k...

Additional to a behavior switching between solid-like and liquid-like, dense granular flows also present propagating grain size-dependent effects called non-local effects. Such behaviors cannot be efficiently modeled by standard rheologies such as µ( I )-rheology but have dealt with advanced models. Unfortunately, these models are still new used easily nor for various configurations. We propose...

The aim of this paper is to present a new well-balanced finite volume scheme for two-dimensional multilayer shallow water flows including wet/dry fronts. The ideas, presented here for the two-layer model, can be generalized to a multilayer case in a straightforward way. The method developed here is constructed in the framework of the Finite Volume Evolution Galerkin (FVEG) schemes. The FVEG met...

The results of an investigation in developing a generalized toolkit for Quadtree based Finite Volume models, exemplarily applied on the Shallow Water Equations, are given in this report. The developed application model: (i) discretizes a given topography using a quadtreebased grid system and (ii) solves the Shallow Water Equations by a numerical method based on the Finite Volume Method on the a...

We present two new large time step methods within the framework of the wellbalanced finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for low Froude number shallow water flows with source terms modeling the bottom topography and Coriolis forces, but results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume form...

This paper deals with intrusive Galerkin projection methods with Roe-type solver for uncertain hyperbolic systems using a finite volume discretization in physical space and a piecewise continuous representation at the stochastic level. The aim of this paper is to design a cost-effective adaptation of the deterministic Dubois and Mehlman corrector to avoid entropy-violating shocks in the presenc...

The modern vision of a flow solver necessarily includes adaptivity. In particular, mesh adaptivity enables the solution strategy to allocate the resources efficiently, in that cells are concentrated in areas where they are needed, as opposed to uniform mesh refinement. Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite successful with finite volume solvers for comp...

We derive a posteriori error estimates for the discretization of the heat equation in a unified and fully discrete setting comprising the discontinuous Galerkin, finite volume, mixed finite element, and conforming and nonconforming finite element methods in space and the backward Euler scheme in time. Our estimates are based on a H-conforming reconstruction of the potential, continuous and piec...

In this paper an evolving surface finite volume method is introduced for the numerical resolution of a transport diffusion problem on a family of moving hypersurfaces. These surfaces are assumed to evolve according to a given motion field. The ingredients of the method are an approximation of the family of surfaces by a family of interpolating simplicial meshes, where grid vertices move on moti...

1. Poisson Equation 1 2. Outline of Topics 3 2.1. Finite Difference Method 3 2.2. Finite Element Method 3 2.3. Finite Volume Method 3 2.4. Sobolev Spaces and Theory on Elliptic Equations 3 2.5. Iterative Methods: Conjugate Gradient and Multigrid Methods 3 2.6. Nonlinear Elliptic Equations 3 2.7. Fast Multiple Method 3 3. Physical Examples 4 3.1. Gauss’ law and Newtonian gravity 4 3.2. Electrost...