All Questions
112 questions
0
votes
0
answers
45
views
Fastest way to check if mesh is structured?
What is the fastest and most efficient way of checking if a mesh is structured?
- 294
0
votes
0
answers
128
views
Heat Equation for fast source with FiPy
I'm trying to solve the following differential equation with FiPy, basically laser irradiation on a surface
$$
\rho_{s}C_{p,s}\frac{\partial T}{\partial t} = k_{s}\frac{\partial^{2}T}{\partial x^{2}} +...
- 11
3
votes
0
answers
53
views
Datasets for inverse heat transfer problems
I was wondering if there is an available, real-life known inverse heat transfer problem dataset to benchmark oneselfs algorithm, as in MNIST for deep learning. Talking about... (well in this case I ...
- 191
1
vote
1
answer
256
views
Coupled Partial Differential Equations
I'm trying to solve the following system of coupled differential equations, the two-temperature model for $e$ = electrons and $l$ = lattice.
$$
\rho_{e}C_{p,e}\frac{\partial T_{e}}{\partial t} = k_{e}\...
- 11
1
vote
0
answers
50
views
How can I apply a mixed boundary condition to a multi-material heat transfer problem using Crank-Nicolson?
I am working on a mixed material model for a melting material and need to enforce both a Dirichlet and Neumann type condition at the interface. Subject to an external surface heat flux at the top of ...
- 11
0
votes
0
answers
38
views
Thermo Hydraulic Mechanical modeling of energy wall slab in Comsol multiphysics
I am currently working on a complex simulation project involving an energy wall slab, and I need assistance in accurately modeling and validating it using COMSOL Multiphysics. Here are the details of ...
0
votes
0
answers
50
views
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
...
- 183
0
votes
1
answer
121
views
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 ...
- 57
1
vote
2
answers
121
views
How to handle non bilinear weak form?
I solved the 2D heat equation using the finite element method. It all went well first with the adiabatic case, however problems occured when I introduced cooling with the enviroment.
I modeled the ...
- 63
2
votes
1
answer
411
views
Where am I making a mistake in solving the heat equation using the spectral method (Chebyshev's differentiation matrix)?
I would like to numerically solve the following heat equation problem:
$$ u_t = \Bigg(2{a \over l}\Bigg)^2 u_{xx} \tag 1$$
$$ x \in [ -1, 1 ] \tag 2$$
$$ u(x, 0) = 0 \tag 3$$
$$ u(1, t) = A \sin \Bigg(...
0
votes
0
answers
68
views
Algebraic Grid Generation
I am new to the topic " Algebraic Grid Generation". I want to find a simple example where we solve the host equation, let us say the heat equation, numerically in the computational domain ...
1
vote
1
answer
338
views
Why does scipy Conjugate Gradient solver fail to converge for non-steady heat equation using Crank-Nicolson method
Could someone please explain why my implementation of the Crank-Nicolson method applied to the non-steady heat equation won't converge? There shouldn't be any nonlinear aspects to my implementation ...
- 13
2
votes
0
answers
114
views
Efficient heat diffusion implementation with varying coefficients
I have the following heat diffusion equation:
\begin{alignat}{3}
\partial_t u(t, \vec{x}) &= g(\vec{x})\Delta u(t,\vec{x}), &\quad& \vec{x} \in\Omega, \, t\in(0,\infty],\\
\partial_n u(t,\...
- 2,892
5
votes
1
answer
107
views
Prediction of sphere (i.e. roast) core temperature heated in an oven
The real-life problem
Assume I put a spherical roast with initially constant temperature of start_temp=25 (°C) into an oven with ...
- 161
1
vote
1
answer
308
views
2D Heat equation solved with finite element method converges in skewed way
I tried to solve the 2D heat equation with the finite element method, using triangles as elements. Currently generated by a Delaunay triangulation. The base function I'm currently using is basically ...
- 63
0
votes
1
answer
143
views
How to get a normalized gradient with FreeFem++?
I am trying to use FreeFem++ to solve the heat geodesics algorithm.
The algorithm is:
solve $\dot u = \Delta u$ at a specific time $t$.
compute $X = \frac{\nabla u_t}{|\nabla u_t|}$
solve $\Delta\phi ...
- 379
1
vote
0
answers
115
views
Accuracy of the Crank-Nicolson method for non-linear, inhomogeneous heat equation
I am currently coding a solution to the following PDE:
$\frac{\partial T }{\partial t} =\frac{\partial}{\partial \theta}(A(\theta ,\phi )\frac{\partial T }{\partial \theta}) +\frac{\partial }{\partial ...
- 11
2
votes
0
answers
113
views
Conceptual doubt regarding 2D conjugate heat transfer modelling (COMSOL and Mathemtica)
I have been dealing with some conceptual flaws in my understanding of modelling, which I will elaborate herein. I am modelling conjugate heat transfer of a reciprocating fluid, which flows with ...
- 41
0
votes
1
answer
206
views
Gmsh Python: Specify mesh regularity conditons
I am using python API of Gmsh to generate a mesh for a rectangular domain. I am really new at this. My code looks like this,
...
- 183
0
votes
1
answer
148
views
Problem with my Octave code (unsteady heat equation with FEM)
I want help with my Octave code regarding the unsteady heat equation.
My geometry and mesh are generated with FreeFEM++, so there is no problem with that (I tried it with the steady problem with no ...
- 3
1
vote
0
answers
64
views
Anisotropic lines identification algorithm
I am implementing an algorithm to identify the anisotropic lines in an unstructured mesh. This is done in the framework of an Agglomeration algorithm for Non-Structured multigrid applied to FV ...
- 410
0
votes
2
answers
416
views
How to create random, unstructured mesh of surface
I am working on a supersonic boundary element method (https://github.com/usuaero/MachLine). In order to test its sensitivity to the boundary discretization, I'd like to be able to create "random&...
- 64
0
votes
0
answers
77
views
deal.II and curved faces: how can I get the curved description
I'm not a deal.II expert, and while studying step-6 I was reading the documentation of the MappingQ1 class in the deal.II documentation. At some point in the description (https://www.dealii.org/...
- 435
2
votes
0
answers
80
views
Centered finite volume scheme for an advective term on an unstructured/irregular/non-uniform grid
Consider the continuity equation
$$\frac{\partial u}{\partial t} + \frac{\partial \Phi}{\partial x} = 0$$
$$\Phi = au + b\frac{\partial u}{\partial x}$$
Suppose I want to solve the above using ...
- 317
2
votes
0
answers
92
views
How to accelerate the computing of implicit finite difference method for heat conduction between two solids
Edit on May 3rd: I have found the problem. Because the difference of between $k_1$ and $k_2$ is huge, a very small time step need to be chosen so that the right green part can "feel" the ...
- 21
0
votes
2
answers
832
views
Which algorithms exist to create a tetrahedral volume mesh from an STL file?
Basically just that. I am trying to write a C++ program that reads in an STL and should compute an unstructured tetrahedral volume mesh based on the surface triangulation given by the STL file.
I ...
1
vote
0
answers
43
views
Simultaneously partition all mesh elements (nodes, edges and cells) among processors
The numerical method that I'm implementing stores various fields in various elements of an unstructured triangular mesh. Data may be stored in cells, nodes and even edges of the mesh. For a parallel ...
- 165
0
votes
1
answer
837
views
Convert unstructured mesh to structured mesh
I need help to know, how can I convert an unstructured 2d mesh for structured mesh? (Software Gmsh version 4.9.3).
This is my script in Gmsh.
...
2
votes
0
answers
294
views
Rosenthal equation for multi track
Rosenthal's equation lets one calculate the temperature profile of a moving point heat source analytically for thin and thick plates. For simplicity I use the equation for thick plates defined as:
$$T-...
- 840
1
vote
1
answer
2k
views
How to solve heat equation in spherical coordinates with finite differences?
I have a problem dealing with heat transfer which is spherically symmetrical. I was thinking it should be possible to solve this as a 1d problem in spherical coordinates using the radius only.
...
- 111
4
votes
1
answer
139
views
Solving geodesics on triangular meshes gives negative distances
I have implemented the heat method for geodesics:
https://www.cs.cmu.edu/~kmcrane/Projects/HeatMethod/paperCACM.pdf
When I run it I am getting a solution that, visually, seems correct:
In this image, ...
- 379
0
votes
1
answer
214
views
Incorporating heat flux into Laplace Equation
I need to find the temperature distribution of a square plate using the Laplace equation by using FDM:
$$ \frac{d^2T}{dx^2} + \frac{d^2T}{dy^2} = 0$$
But there is a heat flux entering from the top ...
- 145
0
votes
1
answer
274
views
Unstructured mesh preprocessing
For solving PDE with self written code it is needed to preprocess the data from mesh generators. I recently started shifting from cartesian grid to unstructured.
I finished reading up to FVM part of ...
- 362
2
votes
2
answers
468
views
Two-dimensional heat equation with Neumann boundary conditions: any hope to find an analytical solution?
I am looking for references showing how to analytically solve the heat equation with Neumann boundary conditions in two dimensions.
So far, I have found the problem solved analytically in one ...
- 61
1
vote
0
answers
193
views
Interpolation of a Concave Mesh
I would like to have an algorithm that interpolates the values attached to nodes in a concave mesh mesh.
To be me precise, assume we have a point cloud P (e.g. in 3 dimensions) and a list of edges E ...
- 119
2
votes
1
answer
227
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 ...
- 832
3
votes
2
answers
215
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 ...
- 645
1
vote
1
answer
56
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 ...
- 13
2
votes
2
answers
219
views
Heat equation in non-dimensional form behaving differently than in usual format
Starting from
$$
c_p \frac{\partial u }{\partial t} = k \nabla^2 u
$$
in a one dimensional domain [0,1] where $c_p$ and $k$ are modeling two different materials:
$$
k =
\begin{cases}
1 ~\text{if} ~x &...
- 601
4
votes
2
answers
701
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 ...
0
votes
0
answers
86
views
How to calculate the interior value of triangular element in edge (vector) finite element?
I was using an edge (vector) finite element to solve electromagnetic diffusion (two-dimensional cases). The element that I used was a triangular element. I have got the result of the finite element in ...
- 9
1
vote
2
answers
674
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 ...
- 304
1
vote
2
answers
811
views
How to use the Thomas-Algorithm to the Heat-diffusion-equation correctly
My post is structured in four parts:
I give you some information about the context my principal questions refer to.
I will tell you what I believe to know about the Thomas Algorithm. If I am wrong ...
- 11
2
votes
1
answer
2k
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 ...
- 304
2
votes
3
answers
553
views
Flux sign and face normal confusion in finite volume method
I implemented a solver for the 2D steady-state heat equation (without heat generation and homogeneous material) $\nabla. (k\nabla T) = 0$, using finite volume method, however, I am having some ...
- 304
1
vote
0
answers
61
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 ...
- 600
2
votes
3
answers
1k
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 ...
- 235
0
votes
1
answer
95
views
Parallel mesh partitioning
When a mesh partitioning takes place and every process works on a part of the mesh is any way to rename the global numbering of nodes(on each process) into a local numbering?Is there any software that ...
- 481
1
vote
0
answers
456
views
Incorporating radiation boundary condition at the edge in finite difference
I am trying to solve the 2-d heat equation on a rectangle using finite difference method. I am confused as to how to incorporate non linear radiation boundary condition at the edge.
$-k\frac{\partial ...
- 19
4
votes
3
answers
1k
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 ...
- 191