# Questions tagged [finite-volume]

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

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### Deriving order of accuracy and interpreting a given discretization scheme when underlying method ( finite difference/volume) not known

If a spatial grid is given with time levels like this: to solve the following model problem Now consider the following discretization schemes: Scheme 1 Scheme 2 Usually, to determine order of ...
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### Moving least square method in finite volume method

Consider a differntial equation like : $\nabla .(\nabla u)=cte$, using finite volume method we can write $\int\nabla .(\nabla u) dv =\int n.(\nabla u) dA$. Here we want to use the moving least square ...
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### Finite volume method for a general flux

How to approximate flux 𝐹(𝑢)⋅𝑛 where 𝑛 denotes the unit normal outward when using finite volumes? in my case it's not a conservation law so my question is how can we approximate the final term \...
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### How to approximate the flux when using finite volumes?

How to approximate flux $F(u)\cdot n$ where $n$ denotes the unit normal outward when using finite volumes? $$\int_{\sigma} F(u) \cdot \boldsymbol{n}_{K, \sigma} \mathrm{d} \gamma(x)$$
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### Discretizing the viscous component in 1 - D Navier stokes compressive flow

I've been working on modelling the NS equations in order to simulate shock waves. The equations are set up on the form: \frac{\partial U}{\partial t} + \frac{\partial F(U)}{\partial x}...
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### QUICK scheme derivation

I am reading about QUICK scheme for calculating the value of unknown variable $\phi$ in finite volume method. Given a locally one dimensional flow, we assume the value of $\phi$ is computed as a 2nd ...
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### How to determine the orientation of convex/concave hexahedra?

I am writing a code that checks the orientation of a list of vertices (along with face connectivity) describing both convex and concave hexahedra. The face connectivity table stores the list of vertex ...
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### Finite Volume on Cubed Sphere

The US weather model uses an uncommon (?) discretization called 'Finite Volume on Cubed Sphere'. To avoid the singularities that occur at the poles when using lat/lon discretization, they instead ...
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### Discretizing Multi-species Ion Exchange Equations by Finite Volume Method

I'm solving a system of multispecies ion exchange equations (diffusion+drift fluxes) in 1-d spherical domain using finite volume method to obtain the ion concentrations at the next time step. After ...
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