12 votes

How can I generate a Swiss-Cheese type region and render it transparent?

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12 votes
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Solving Burger's equation with NDSolve at large time

Similar problems have been discussed in this site for several times: Solution of Burgers equation with some initial data 1D Euler equations (fluid dynamics) with NDSolve Circumvent NDSolve::bdord: ...
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10 votes

Solving Burger's equation with NDSolve at large time

The answer of Nasser is only in parts correct. The analytic/implicit solution $$ u(x,t) = f(\xi) = f(x-ut), \quad \xi = x - f(\xi) t $$ is only the physical solution in the interval $0\le t \le t_b$ ...
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9 votes
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NeumannValue is producing incorrect results

This is a bit funny. It's not NeumannValue that's causing trouble. It's all because you've specifying the DirichletCondition in ...
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9 votes

Solving Burger's equation with NDSolve at large time

Following the example set by xzczd's answer: an alternative to an external library would be to implement a simple shock capturing finite volume scheme like the one put forward in New High-Resolution ...
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Reproducing figure from paper on hydrodynamics

We can't reproduce picture from the paper cited since they used Fourie integral on $-\infty \le x \le \infty$. With FEM we can reproduce part of picture be crossing side vortexes as follows ...
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7 votes

Coupled PDE using NDSolve

To solve this problem we can use FEM as follows ...
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Neumann boundary conditions are not satisfied

Not sure how to explain the non-convergence of phisol'[0]. (Though phisol'[0] == -0.0302716 is close to zero, it won't get ...
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6 votes

Droplet of water-alcohol mixture spreading due to evaporation-caused surface tension gradient

At least 3 issues here. You're handling the cylindrical coordinates in an unsual way i.e. setting domain of definition of r to $r\in(-\text{boundary},\text{...
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6 votes

How can I generate a Swiss-Cheese type region and render it transparent?

One way: Show[BoundaryDiscretizeRegion[cheese, MaxCellMeasure -> 0.001]] /. FaceForm[Directive[d__]] :> FaceForm[Directive[d, Opacity[0.5]]] Another way: <...
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6 votes

Solving Burger's equation with NDSolve at large time

I am not sure if there are options to improve NDSolve. I tried stiffness method, but that did not help. But since the inviscid Burgers' equation has analytical solution, then you can use that. Where $...
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4 votes

Using Neumann boundary conditions for the wave equation

With NeumannValue the absorbing boundary conditions might be formulated for x==2and x==-2. ...
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2 votes

NDEigensystem with FEM: parasitic solutions

The symmetric model considered in the post is numerically unstable. The numerical scheme is stabilized by, physically speaking, detuning the dispersion of two electron bands: $\pm M \pm B q^2 \to \pm ...
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2 votes

Using Neumann boundary conditions for the wave equation

As mentioned in the comment above, the problem is related with (and essentially equivalent to, in my view) this one, but let me elaborate with an answer anyway. The explanation for the usage of ...
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Speeding up Boussinesq equations solving?

We use scaling as in our model on this page.See also Vahl Davis, G.de (1983) : Natural convection of air in a square cavity : A bench mark numerical solution. Int. J. Numer. Methods Fluids 3, 249-264. ...
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2 votes

Convert boundary condition involving derivative to NeumannValue programmatically

The following my (incomplete) attempt. ...
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2 votes

How to solve 2D eigenvalue problem with robin boundary conditions

Let me extend my comments to an answer. …it seems it has issues with non-homogeneous boundary conditions Yes, but your b.c.s are homogeneous. NeumannValue can ...
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1 vote

How to solve 2D eigenvalue problem with robin boundary conditions

Unfortunately NDEigensystem doesn't evaluate. Perhaps NDSolveValue helps to describe the system with Robin boundaries and gives ...
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