Questions tagged [unstructured-mesh]

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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 ...
16
votes
1answer
244 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, ...
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 ...
10
votes
3answers
1k views

N-dimensional Delaunay Tesselation Software Libraries

I have a set of known points/nodes irregularly spaced in N-Dimensional space (N>=2), and I would like a way to generate the Delaunay triangulation of these points, and return the corresponding ...
7
votes
2answers
604 views

Mesh ordering algorithms used by COMSOL Multiphysics

Ordering of elements in an unstructured mesh is undoubtedly very important for the performance of computations. For example, it determines the structure of sparse matrices arising from PDE ...
6
votes
2answers
641 views

Unstructured mesh vs hybrid structured/unstructured for numerical simulations

While answering one of the questions on meshing process, I encountered a lack of understanding on my end for the comparison of the mesh quality. First, consider an unstructured mesh created in GMSH ...
6
votes
1answer
220 views

Working with large mesh files

I am working on some medium to large scale finite element codes. By using established and available tools I am able to have an algorithm that scales well up to about 10,000 cores. Investigating ...
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 ...
6
votes
0answers
352 views

Are there well-known methods for navigating on kd-trees?

When you have a mesh, there are many well-known methods to navigate it, as for example using a half-edge data structure, that allows easy circulation around faces and vertices. Are there similar ...
5
votes
2answers
1k views

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_{...
5
votes
1answer
240 views

Largest unstructured mesh problem solved till date

What is the largest problem (in DOF) that has been solved till date using a fully unstructured mesh. I know about PFLOTRAN but I am not sure if it is the largest. If someone can point to relevant ...
5
votes
1answer
556 views

Finite volume a posteriori error estimation

I'm wondering what alternatives there are to a grid convergence study to judge solution accuracy for a given grid resolution when doing steady-state RANS simulations on an automatically generated ...
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 ...
4
votes
2answers
173 views

Meshing surface of a sphere with a subdomain

I am trying to build a triangle mesh of the surface of a sphere which also includes a subdomain defined by a 'polygon'. Here is a successful example (subdomain defined by the red dots): Note that the ...
4
votes
1answer
558 views

unstructured grid AMR

Are there libraries for conducting parallel AMR on an unstructured grid ? For a finite volume code, polyhedral cells with arbitrarily shaped faces are as easy to handle as hexahedra, and infact ...
4
votes
0answers
472 views

Large meshing with tetgen

So I have a point cloud that I am creating a 3D flat rectangular surface from. I'm then turning it into a hollow box and connecting the corners by just dropping this surface mesh down. I need it to ...
3
votes
2answers
247 views

Why FVM can handle unstructured meshes while FDM cannot?

How come Finite Volume Method(FVM) handle the unstructured meshes and Finite difference Method cannot, whereas in FVM to approximate the fluxes at the boundary we use the central differencing? My ...
3
votes
1answer
330 views

Is there any open-source code for a hybrid 2D mesh (triangles and quadrilaterals)?

The question is pretty much the title. Note that I have lots of experience using open-source meshing tool, e.g. Gmsh and OpenFoam blockMesh & snappyHexMesh. Nevertheless, I have no idea on how to ...
3
votes
1answer
103 views

number of tetrahedra in unstructured mesh when edge length is halved

For a given 3D domain, two unstructured tetrahedral meshes M_1 and M_2 are generated. The average edge length in M_1 is double the average edge length of M_2. Are there estimates on the ratio of the ...
3
votes
1answer
129 views

Mesh with constraints

Is it possible to construct a constrained tetrahedral mesh of a domain using Tetgen or similar software? What I mean by constrained is that there are some nodes or edges that are not free but are ...
3
votes
1answer
382 views

How to enforce the boundary conditions

I want to solve a poisson problem on two domains,(interface problem: Let $\Omega $ be a square, $\Omega=\Omega1 \cup \Omega2$ and let $\Omega1$ be a circle inside the square. $\Gamma$ is the boundary ...
3
votes
0answers
251 views

Why wall shear stress calculated from LBM directly and the one calculated based on velocity profile are so different in some cases?

First of all, I hope you accept my apologizes if my question seems off topic here. But, I asked this question in ParaView forum and after a week still I did not receive any response yet, so I'm ...
2
votes
4answers
2k views

Computing the derivative on a mesh

I have a 2-D mesh of triangles and I have a scalar function $f(x,y)$ defined at all the vertices of this mesh. I want to accurately estimate the values of $\frac{\partial f}{\partial x}$ and $\frac{\...
2
votes
2answers
174 views

Is there a bound on the number of edges, facets, and elements in a 3D simplicial mesh in terms of the number of mesh nodes?

I am currently working on a 2D finite element code with a mesh that contains duplicate nodes at certain interfaces where jumps occur. In order to set up the appropriate linear systems, I have to take ...
2
votes
2answers
103 views

How to find out the difference between a structured and unstructured mesh using the file containing the mesh information?

I have two different mesh files (both are .inp files obtained from Abaqus) that represent the exact same geometries with the same boundary conditions, etc. The only difference is that one of them is ...
2
votes
2answers
520 views

Getting adjacent cells map for an unstructured polyhedral mesh

I am doing a little project on solving the heat equation using finite-volume method on a solid cube, I converted the polyhedral mesh of the cube to an OpenFOAM mesh. I have a Python code where I ...
2
votes
1answer
111 views

Partition mesh into predetermined submeshes

I have a mesh already partitioned into disjoint groups of cells. What I want to achieve is the following. Obtain the adjacency graph for the cell groups. Partition the mesh, i.e. generate submeshes ...
2
votes
1answer
331 views

How to calculate skewness for a mesh?

I am writing a code to calculate mesh quality stats such as: cell volume, face areas and non-orthogonality between faces (basically something like OpenFOAM's ...
2
votes
3answers
241 views

How is central difference scheme second-order accurate?

In an arbitrarily unstructured mesh, shown in the figure below, in the context of finite volume method, I want to obtain an approximation of $\phi_f$, where $N$ and $P$ are cell centers of adjacent ...
2
votes
1answer
131 views

Location of Unknowns in Unstructured Mesh

I am currently learning a code which utilizes Scharfetter-Gummel discretization for unsteady drift-diffusion equations. For this scheme, a 2D unstructured triangular mesh is used, with the unknowns ...
2
votes
1answer
84 views

Developing a meshfree contouring algorithm

I would like to find the contours of a scalar function $u(x,y)$ available as a discrete set of function values $u_i = u(x_i,y_i)$ over a scattered set of points $(x_i,y_i), i=1,...,N$. In my case, the ...
2
votes
0answers
130 views

scalable parallel mesh/amr on unstructured grid

I am trying to code a scalable parallel AMR for unstructured grid. There seems to be three approaches for this a) Store some global grid info on each processor and partition with parmetis (The ...
2
votes
0answers
27 views

Choosing suitable polynomial degree based on information in advection stencil

I'm working on a finite volume advection scheme for unstructured meshes which uses a multidimensional polynomial weighted least squares fit for interpolating from cell centres onto faces. In 2D, the ...
1
vote
3answers
606 views

Parallel solver for sparse matrices on unstructured grids

I am trying to solve Euler equations on unstructured grids. Consequently, the problem reduces to solving Ax=b where A is a ...
1
vote
1answer
86 views

Common nodes in two FEM grids

There are two independent tetrahedral FEM grids. Second grid is subset of the first. By subset, I mean: nodes from the second grid are exactly in the same positions as some nodes from the first grid. ...
1
vote
1answer
190 views

Jacobian matrices on unstructured grids: underlying map?

Suppose I have an unstructured polygonal mesh system like so: Each node $x$ has Cartesian coordinates $(x_1,x_2)$, so for a given node can form matrices like this: $$ J(x,y,z) = \left(\begin{array}...
1
vote
1answer
39 views

How to evaluate the average value of a polynomial inside the triangle area in finite volume sense?

Consider we have a linear bivariate polynomial: $$p(x,y)=ax+by+c.$$ To construct the linear polynomial using least square method, we need to evaluate the value of the average polynomial $p$ in at ...
1
vote
1answer
123 views

How to compute gradient of a cell having a boundary face?

In many situations in unstructured mesh solvers, one needs to compute gradient of arbitrary variable $\phi$ such as temperature or velocity at face centers (one of such situations is correction for ...
1
vote
1answer
396 views

How I could calculate L2 norm of an unstructured grid?

I want to calculate L2 norm of a 3D unstructured grid to compare my simulation results in two different mesh sizes as coarse and fine. I read this answer and it seems in three-dimensional space, I ...
1
vote
1answer
212 views

Libraries to deal with unstructured grids

I am dealing with a *.cgns file. This mesh format, when saved as an unstructured grid, holds nodes coordinates, nodes connectivity per element and boundary ...
1
vote
1answer
543 views

Convert Unstructured Mesh to Structured

I have solved a simple problem on Openfoam, which is a 3D rectangular parallelopiped, filled with rectangular hexahedrons as mesh elements. The structured, mapped mesh was made in ICEM and solved in ...
1
vote
1answer
208 views

Conceptual question about fitting of scattered data

What are the problems that arise when fitting (2D or 3D) a set of scattered data? (non uniformly distributed) I had some data I had to fit and I solved the problem using the ...
1
vote
1answer
400 views

Number of faces in a 3D multi-type unstructured grid

Given a 3D unstructured grid consisting of mixed types of shapes (hex, tet, ...), is there a method to know how many faces (including boundary faces) are contained in the grid?
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) ...
1
vote
0answers
40 views

Stress visualization for structured and unstrcutured mesh

I put together a FEM solver to do some structural analysis. At the moment I am trying to add stress visualization feature to my code. The post-processing is done with Paraview and the results with ...
1
vote
0answers
55 views

Combining fluid flow solver based on lattice Boltzmann method with a mechanical deformation solver based on finite element method

I'm thinking to couple my fluid flow solver based on lattice Boltzmann method with a mechanical deformation solver based on finite element method to take account for solid deformation in my models. In ...
1
vote
0answers
59 views

Efficient initial identification of solid or liquid domains for a block structured Cartesian grid generation system

INTRO Within the last 5 days I was able to generate a block structured Cartesian grid generation system with a combination of Fortran,C++ and Python. I am running intersection tests of the ...
1
vote
0answers
139 views

BTCS-like method for heat conduction in unstructured triangular grid

I want to write a simple simulation for heat conduction in a unstructured triangular mesh. I already made it work for a structured rectangular grid with the ADI method, but now I need more complex ...
0
votes
1answer
838 views

C++ library unstructured mesh writer to VTK format (or similar)

I am working on a 2D unstructured code in C++. I am using gmsh to generate a 2D unstructured mesh and reading it into my program with a library called ...
0
votes
2answers
881 views

2D mesh generator with geometric primitives

The question is exactly as the title: Which 2D (triangular) mesh generator software can be used which has a set of geometric primitives, controlled mesh size and standard output (.vtk or something ...