Questions tagged [finite-volume]
Referring to the discretization of partial differential equations using Finite Volume Method.
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What is the best finite volume method for the following equation?
I'm trying to create a partial differential equation that approximates 1-D climate in a rocky planet's atmosphere, which accounts for energy transport via radiation and convection. I am only ...
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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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Lowest order Raviart Thomas elements
I have questions regarding the implementation of Lowest order Raviart Thomas elements on quadrilaterals, some papers use the basis functions in this form:
for example the right edge: $N = \left[\dfrac{...
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Finding neighboring cells using Gmsh API
I am creating a simple mesh on a square domain, $[-5,5]\times[-5,5]$ using the following .geo file
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Need help with adaptive meshing code
I am trying to understand adaptive meshing and is using this code (https://github.com/esquivas/amr1d) as a reference. However, there is no documentation for it and thus, it is hard for me to ...
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numerical schemes for 1D PDE: for smaller grid size there is an increased roundoff error, larger size more truncation, so sweet spot in between?
I had a discussion with a colleague today. He claimed that usually for a general numerical scheme for solving a general 1D PDE, for smaller grid size there is an increased roundoff error because of ...
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Generating unstructured finite volume mesh
I want to generate a triangular mesh over a rectangle domain in order to solve Euler equations. Most mesh generator generate a mesh while providing node connectivity for each element. This is ...
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Creating nonuniform grids for FDM with multiple points of concentration
If I am creating a grid in the $S_i$ direction with $N_S+1$ grid points. If I want more steps around some $K$, I can use:
$$
S_i=K+c \sinh \left(\xi_i\right), \quad i=0,1, \ldots, N_S
$$
where $c=\...
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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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Non-standard boundary condition for incompressible Navier Stokes
I am having difficulties applying the boundary condition
$$\frac{\partial \vec{V}}{\partial t} + u\frac{\partial \vec{V}}{\partial x} = \frac{1}{\operatorname{Re}}\frac{\partial ^2 \vec{V}}{\partial y^...
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Burger's equation (PDE) does not work with downwind difference?
I'm working on implementing the discretised Burger's equation. I am quite confused as to why it does not work when using a step-function and downwind difference formula. When using a step-function and ...
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FVM for non-regular domain with triangular mesh
Setup
The 1D convection-diffusion equation is given by:
\begin{equation}\tag{1}
\frac{\partial u}{\partial t} + v \frac{\partial u}{\partial x} - \mu \frac{\partial^2 u}{\partial x^2} = 0,
\end{...
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Adding a diffusion term to the MUSCL - Kurganov and Tadmor central scheme
Im currently using a MUSCL scheme with a rusanov flux and Van Leer limiter to simulate the 2d euler equations:
$$ \frac{\partial \rho}{\partial t} + \frac{\partial \rho v_x}{\partial x} + \frac{\...
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