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Starting configuration for Molecular Dynamics

Usually one needs to employ periodic boundary conditions (at least in the horizontal directions). Any atoms which fly outside of the box will be mapped to the opposite side. This also has to be ...
• 3,005
Accepted

Dirichlet condition in finite element method

From a different perspective, regardless of where a system $A\cdot x = 0$ comes from (does not have to be FEM), if you change your mind and would like to prescribe part of $x$, then you'd necessarily ...
• 1,008
Accepted

How to evaluate the points near/at the boundary when using Richardson extrapolation for improved accuracy of a derivative

Your question was quite interesting - I haven't seen it addressed in any of the books on FDM that I have read (LeVeque, Morton, Lapidus, Thomas). I had never thought about this, so I tried to come up ...
• 2,302
Accepted

Why do we use modified pressure in incompressible multiphase solvers with gravity?

It has been a long time since I was involved in the details of developing CFD codes, but here goes: Writing general purpose CFD solvers is pretty difficult because the range of problems that the code ...
Accepted

• 362
Accepted

How to handle non bilinear weak form?

From your formulation it's still unclear what are the boundary conditions. But from the sentence about replacing $n\cdot \nabla u$ with $h(T_{\infty} - u)$ and your comment it sounds like your ...
• 2,302

How to handle non bilinear weak form?

You can move the term with $h T_\infty v$ to the right hand side so it becomes part of the linear form and the load vector.
• 2,104
Accepted

How to calculate the force of solid applied by fluid? Using finite difference method, DNS, staggered grid, SIMPLE algorithm, immersive boundary

The question is solved. I use wrong coefficient formula. I should use 2d formula but actually I use 3d. And my calculation method using momentum conversation may be wrong, but that is fine, I can use ...

How to impose boundary conditions when solving a nonlinear dynamical system given by the FEM solver

The general approach in a Newton method is to solve for increments $\delta u$. Then, if your current solution already has the right values at the boundary, $\delta u$ needs to have zero boundary ...
• 56.1k
1 vote
Accepted

How to obtain the transfer function between boundary condition and point of wave equation?

In order to calculate the transfer function one can assume that $f(t) = e^{s\,t}$, with $s$ representing the Laplace variable. Using separation of variables $u(t,x) = T(t)\,X(x)$ in $(1)$ yields  \...
• 470
1 vote
Accepted

Are there necessary conditions for SOR algorithm to converge when used for 2D discrete Poisson problem, with PBC, besides solvability condition?

You are trying to solve a Poisson problem with periodic boundary conditions. As you know, it only has solutions when the integral of the source term is zero. However, due to finite precision ...
• 514
1 vote

Dirichlet condition in finite element method

After some studies, I want to provide an example of a case where it can be shown that the submatrix $K$ as described in my question is actually positive-definite, not just positive-semidefinite. ...
• 145
1 vote

First derivative central differences with reflecting boundary conditions

The factor 2 arising in the approximation of $\partial_x u_1$ and $\partial_x u_{n+1}$ is correct. It is correct because you are discretizing your boundary conditions ($\partial_x u_0$ and \$\partial_x ...

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