Questions tagged [unstructured-mesh]

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5
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2answers
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First order finite volume spatial discretization of the heat equation on an unstructured triangle mesh

Consider a scalar field $u$ on an unstructured triangle mesh which is constant on each face. Let $A_i$ be the area of triangle $T_i$, $N(i)$ the set of triangles sharing an edge with $T_i$, and $L_{...
16
votes
3answers
5k views

Finding which triangles points are in

Suppose I have a 2D mesh consisting of nonoverlapping triangles $\{T_k\}_{k=1}^N$, and a set of points $\{p_i\}_{i=1}^M \subset \cup_{k=1}^N T_K$. What is the best way to determine which triangle each ...
4
votes
1answer
2k views

Is there a mesh generator that will generate zero thickness elements for interfaces?

I have a geometry and a finite element method where there are a couple internal interfaces across which I want to enforce some fairly simple jump conditions. One recommendation I've gotten has been ...
16
votes
1answer
245 views

Usefulness of elements with mesh-dependent stability

After doing some mathematics related to the stability of elements in 3D Stokes problem I was slightly shocked to realize that $P_2-P_1$ is not stable for an arbitrary tetrahedral mesh. More precisely, ...
6
votes
1answer
1k views

Grid mapping from an unstructured triangular mesh to a regular rectangular mesh

I am modeling fracture propagation using a 2-D dynamic unstructured grid. As the fracture propagates over time, the elements move accordingly. For a given time step, I would like to interpolate the ...
11
votes
2answers
2k views

How to interpolate multipoint data to the cell centres of an unstructured mesh?

I have sets of multipoint field data, each point data set relates to a single cell of an unstructured mesh. The goal is to interpolate the data to the cell centre, directly or indirectly, in the most ...
1
vote
0answers
76 views

Advection equation boundary conditions in 2D unstructured grid

Currently struggling with boundary conditions for 2d advection equation. left dirichlet u = (1,0) bot top dirichlet u = (0,0) right neumann du/dx = (0,0) ...