Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [finite-volume]

Referring to the discretization of partial differential equations using Finite Volume Method.

The finite-volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. The method is widely used in Computational Fluid Dynamics codes.

See Wikipedia page on FVM.

271 questions
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Is it necessary to do characteristic decomposition to solve 2D Euler Equation?

Recently, I am trying to solve 2D Euler Equation using FV-WENO reconstruction. For the smooth initial problem, component-wise WENO reconstruction works well. My problem is, if I want to solve double mach reflection problem, do I need to do…
fois
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Interface Conductivity for Finite Volume Method Heat Transfer in Cylindrical Coordinates

I'm solving a heat conduction problem in cylindrical coordinates with a composite cylinder made of two different materials. Essentially the cylinder is split into a central cylinder of material A, surrounded by an annulus of material B. My mesh is…
user34866
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How to approximate flux (with gradient) when using finite volumes?

In finite volume method one is using cell averages. In nonlinear conservation laws discontinuities can be created in the solution process. How to compute the flux when the flux contains a gradient and the Taylor approximation is not valid due to…
delta5
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Finite volume method

I have question connected with finite volume method. Consider equation $$\frac{\partial u}{\partial t}=\operatorname{div}A\nabla u +f . \quad x\in \overline{B}_{1} (0)\subset \mathbb{R}^3 -\text{unit ball with its boundary}$$ I solved IBVP for this…
cool
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What determines the order of a finite volume scheme?

I often hear that cell centred finite volume is second order accurate but at the same time I come across notions of high order FVM flux schemes. Is there a distinction between the two? If I were to use something like a first order upwind referencing…
CuteCompute
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Is upwinding needed for slope limiter / flux limiter and numerical flux?

I have a cell centered cartesian grid and am trying to implement the flux inside the divergence term using numerical flux with a flux limiter. I found different formulas for MUSCL flux limiter, where one source seem to say one needs to use a…
Emil
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Conservative FV Immersed boundary method for compressible flow

Is there a conservative FV second-order (or first-order) accurate immersed boundary method for compressible flow including moving boundaries (in the literature)? By compressible flow I mean the Navier-Stokes eqts. for an ideal gas. Most of the…
gnzlbg
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Effect of Normalization in Unknowns

When solving a FV formulation of a set of equations, a code I am currently working with has user defined normalization factors for scaling equations. It normalizes time, number densities, potential, and fluxes, each with a different factor. I…
Godric Seer
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Finite volume method on a nonuniform grid

I would like to ask a question on the implementation of finite volume method on a non-uniform grid in solving Navier-Stokeq equations. I will just post the screenshot of a PhD thesis, where I found the evaluation of the derivative term difficult to…
jengmge
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Roe Riemann solver for perfect gas mixture

I have working program for solving one-component 1D Euler equations with Roe's approximate Riemann solver constructed according to this pdf. My implementation of the algorithm is as follows ($\rho$ is density, $u$ is velocity, $h=\frac{e+p}{\rho}$…
omican
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Finite volume method implementation issues

I am trying to write a simple finite volume method code but there are some concepts I'm still not really getting right (perhaps I'm overcomplicating things) Given a uniform grid, the idea is to approximate the solution by computing cell averages…
BRabbit27
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Finite volume reconstruction techniques

For a cell-centered finite-volume calculation, with a nontrivial stencil (either using an unstructured grid or a strongly non-uniform structured grid), what are the main techniques for reconstruction of function values and derivatives on cell faces?…
Maxim Umansky
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Matlab CODE of ADER scheme

I read ADER WENO Finite Volume scheme for hyperbolic conservation laws with source term. I want to implement this method in Matlab coding. I got some problems in coding during to computation of numerical flux. Please help me the Matlab…
jixon
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Concave Cells and Finite Volume Method

I would like to know how to compute the "best" cell center for pressure calculation in case of concave polyhedral cells, if it makes any sense. My face centers are defined as faces barycenters and I'm just wondering how to correctly determine the…
Tom
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Problem with cell size and boundary conditions in transient cylindrical conduction

I am attempting to model the steady state behavior of a cylinder using the finite volume method (FVM) subjected to a variety of boundary conditions in Matlab. First off, I am treating the cylinder as being axisymmetric so I am only determine the…
Greg Harrington
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