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Mesh generator ToElementMesh allows to resolve internal boundaries of the domain to be tesselated: << NDSolve`FEM` bmesh = ToBoundaryMesh[ "Coordinates" -> {{0, 0.5}, {0., 0.}, {1., 0.}, {1., 1}, { …

I am trying to simulate heating and melting of the steel plate by means of FEM.The model is based on nonlinear heat conduction equation in axial symmetry case. The problem statement is the next: $$ \ …

Suppose that upper body is ideally rigid and provides support of roller type in connection area. Also assume that contact area is very small compared with characteristic dimensions of the system. Thus …

You can get solution values in nodes by TemprArray = TFun[[4]] {200., 200., 200., 200., 200., 200., 200., 200., 200., 200., 200., \ , 124.242, 127.273, 127.273, 130.303, 130.303, 130.303, \ 124.242, …

We can make use of low level FEM programming tools for FE matrixes calculation but load vector let's calculate "by hands". For load vector we have: $$b_i=\int_{0}^{L}g(t)\delta(x-a)\phi_i(x)dx=\begin{ …

As mentioned user21 for setting traction boundary conditions we need to know normal and tangent to the surface which is subjected to loading. On the inner surface ($r=a$) for the unit tangent vector w …

As far as I understand the main problem deals with big computational time required for determination of average wall temperature of the channel in given cross section. It can be ascribed by the fact t …

Let's the velocity, temperature and pressure are measured in units $u_0,\, dq/k_s,\, \rho u_0^2$ respectively, time and space coordinates are measured in units $d/u_0$ and $d$. In this case the govern …

I am trying to run the element mesh generator DistMeshfrom FEMAddOns package by using version Mathematica 13.2 under Ubuntu 20.04. Needs["FEMAddOns`"] DistMesh[Disk[]] and got the next messages: an …

Function MergeMesh from MeshTools package allows to join separate meshes. Let's take advantage of this useful function for this problem. Needs["MeshTools`"] L = 0.050; d = 0.003; e = 0.005; delta = 0. …

One can also consider the 3D statement of the problem. Solution of a such linear problem is not so time consuming nowadays. For mesh generation let's take advantage of OpenCascadeLink procedures whi …

It seems that the main challenge in this problem is Dirichlet BC which should be switched periodically on $x=0$ and $x=L$. I don't know whether it possible to switch BC inside NDSolveValue but we can …

We can use this code for the case when inflow velocity is constant in time. The flow and temperature field in this system will to come to equilibrium after some period. The non-dimentional governing e …