Questions tagged [finite-volume]

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

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17
votes
1answer
14k views

How should boundary conditions be applied when using finite-volume method?

Following from my previous question I am trying to apply boundary conditions to this non-uniform finite volume mesh, I would like to apply a Robin type boundary condition to the l.h.s. of the domain (...
11
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3answers
4k views

Applying Dirichlet boundary conditions to the Poisson equation with finite volume method

I would like to know how Dirichlet conditions are normally applied when using the finite volume method on a cell-centered non-uniform grid, My current implementation simply imposes the boundary ...
9
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1answer
2k views

PDE discretization with the method of rothe and the method of lines (Modular implementation)

The Heat equation is discretized in space with FV (or FEM), and a semi-discrete equation is obtained (system of ODEs). This approach, known as the method of lines, allows to easily switch from one ...
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2answers
2k views

The meaning of conservative discretization in Galerkin FEM and Discontinuous Galerkin

I do understand the meanning of "conservative discretization" within the FVM/FDM framework, indeed it is well explained in this post. Now, according to the table in this slide (pp.8), it concludes: ...
4
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1answer
3k views

Comparison of Lattice Boltzmann Method vs Traditional Navier-Stokes based Methods

I have a choice of two options, analysing and implementing Lattice Boltzmann methods or traditional Navier Stokes based methods. I'm a CFD newbie and I have a rough idea (though not rigorous enough to ...
53
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3answers
35k views

What are the conceptual differences between the finite element and finite volume method?

There is an obvious difference between finite difference and the finite volume method (moving from point definition of the equations to integral averages over cells). But I find FEM and FVM to be very ...
11
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3answers
2k views

How should non-constant coefficients be treated with finite-volume first order upwind scheme?

Starting with the advection equation in conservation form. $$ u_t = (a(x)u)_x $$ where $a(x)$ is a velocity which depend on space, and $u$ is a concentration of a species which is conserved. ...
5
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2answers
3k views

Does the finite element method impose any restrictions on the Peclet number for numerical stability?

Background on finite volume method When discretising the flux with a central difference stencil of the the advection-diffusion equation restriction $\frac{ah}{d} < 2$ must be observed for the ...
6
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3answers
325 views

Is there a minimum angle requirement for cells in the finite volume method?

In his talk "What is a good linear finite element?", Shewchuk states that small dihedral angles in linear tetrahedra elements cause ill-conditioning of the stiffness matrix. Do small dihedral angles ...
9
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2answers
994 views

Peculiar error when solving the Poisson equation on a non-uniform mesh (1D only) finite volume method

I have been trying to debug this error the last few days I wondered if anybody has advice on how to proceed. I am solving the Poisson equation for a step charge distribution (a common problem in ...
8
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2answers
914 views

Is there a good tutorial or textbook-like source on implementing ENO/WENO with limiters in one (and more than one) dimension?

I've inherited a finite volume code that does a second-order discretization of flux terms for a set of mixed parabolic-elliptic equations with discontinuous diffusion coefficients. The impression I ...
7
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1answer
889 views

Are we free to choose the position of ghost cells on a non-uniform finite-volume mesh?

Following Hundsdorfer approach the finite volume discretisation of the advection-diffusion equation (conservative form) on non-uniform cell centered grid can be written as, $$ w_j^{\prime} = \frac{w_{...
6
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2answers
2k views

Finite-volume method: can Dirichlet boundary conditions be applied to the integral form?

I would like to apply Dirichlet conditions to the advection-diffusion equation using the finite-volume method. This answer, "How should boundary conditions be applied when using finite-volume method?" ...
5
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1answer
2k views

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 ...
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0answers
369 views

Euler Equation Eigensystem with Gravity in the Energy Flux

I am modifying a conservative form of the Euler equations with gravity in the energy flux (see previous question: Energy Conservation in Conservation Laws with Source Terms) for use in a Riemann ...
2
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1answer
244 views

FVM - virtual node discretisation

I have come across the paper titled: A monolithic fluid structure interaction algorithm ... For a 1D grid, at the boundaries the paper uses virtual nodes $x_{0}$ and $x_{N+1}$ (page 372) and for ...
5
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0answers
88 views

Interface Formulation at Finite Volume Boundaries when using the Dual Mesh

When using the dual mesh (vertex-centered) for finite volume methods, you end up with a cell center at the boundaries between materials. It is possible that the equations being solved in each ...
3
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1answer
775 views

Add User-defined/custom differential equations in OpenFoam (CFD)

I am new to OpenFoam. And I am trying to add a set (user defined) of differential equations to OpenFoam. I want to solve this user defined set of equations at each time point in addition to standard ...
3
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2answers
424 views

Energy Conservation in Conservation Laws with Source Terms

I'm wondering if anyone can help me understand energy conservation when using conservation law methods (i.e. Riemann solver, High-Resolution Wave-Propagation Methods) with the addition of source terms:...
3
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1answer
330 views

Finite volume with cell averages vs cell totals for conservation equations

What implementation details need to change if I use a cell average approach rather than a cell total approach for the finite-volume method? For example, consider the conservation law, $$ u_t + \...
3
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2answers
443 views

Finite Difference and Finite Volume as special cases of Finite Element

I have heard this many times that "FD is a special case of FE" and separately, that "FV is a special case of FE". However I have never come across a brief document that substantiates that claim, ...
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0answers
61 views

Discretization used for steady linear elasticity - followup to previous question

This is a follow-up of my previous scicomp question (https://scicomp.stackexchange.com/posts/28863/edit). I figured I'd start a new thread on this as the question is a bit different from my previous ...
1
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1answer
160 views

TDMA with 3rd order upwind scheme

I'm trying to implement a model I found in a paper, but there is something I do not understand. The authors say they use TDMA to solve their equations; however, they use a 3rd order upwind biased ...
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0answers
79 views

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 ...
1
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1answer
146 views

How to compute turbulent energy cascade

I need to compute the kinetic energy cascade using a finite volume solution in an equally spaced grid. I wonder if it is more correct to first compute the kinetic energy in the space (or time) domain, ...