# Questions tagged [finite-volume]

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

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### What can be done with Finite Element Method and not with the Finite Volume Method, and vice versa?

What are some applications where you would absolutely go for either FEM, but not FVM, or vice versa? What are some applications where both methods are equally suited? I worked with the FEM so far and ...
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### Order of accuracy of FVM discretization

I've recently got interested in CFD and started a small project by solving the radial Reynoldsequation. Why the Reynoldsequation? I recently encountered it through my studies and somehow got stuck :) ...
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### Is it generally unstable to use in multidimensional simulations finite difference schemes with higher orders than 2?

I'm part of a team trying to generalize a 1D Advection-Diffussion-Reaction code we inherited by extending it to 2D by using dimensional splitting, i.e. solving advection and diffusion for x and y ...
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### 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 ...
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### Two-dimensional modelling of a flate-plate reactor

I am trying to simulate the unsteady pollutant concentration along the reactor by solving the 2nd order PDE below with the stated BC and IC. which method is appropriate to solve convection-diffusion-...
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### Convection equation expanded in Legendre polynomials

In some areas of physics, for example radiation transport in plasmas, it is beneficial to re-express the convection equation in terms of a Legendre polynomial expansion. This results in a set of ...
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### How to avoid density getting "deleted" in two way rigid body coupling with LBM CFD?

I've been reading this paper recently, which talks about using Lattice Boltzmann methods and two way coupling. Specifically, it outlines fluid solid coupling, and solid fluid coupling, and how simply ...
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### Grids for atmosphere simulation with finite volumes on the globe

I am currently in the early construction process of building a simple CFD model of a rotating planetary atmosphere. The planet should be allowed to tilt significantly, so that a time-dependent source ...
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### Discretizing a parabolic PDE with finite volume method

I want to discretize the following parabolic PDE: $$u_t = \nabla\cdot(\alpha(x)\nabla u)- \beta u\\ x\in\Omega \subset \mathbb{R}^2\\ \partial_n u = 0\\ u(t,0) = u_0(x)\ge 0, \alpha(x)>0$$ Given ...
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### Choice of velocity grid - staggered or not?

I'm trying to understand when and why one would use a staggered vs. a colocated grid in problems that have velocities and scalars that they transport (e.e. density). If scalars are defined cell-...
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### FEM/FVM/FD for structural modeling and stability issues due to large structural constants?

I've read that in modeling structures problems, the finite element method (FEM) is typically used. I am unfamiliar with FEM, but I am wondering, in particular, if using FEM, as opposed to finite ...
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### Implement Robin boundary condition (finite volume)

I have a PDE equation with Robin Boundary condition in an annulus system and I should solve it by finite volume method: \begin{align} \frac{\partial T_f}{\partial t} - k \left(\frac{\...