# Questions tagged [numerical-modelling]

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### Can one publish a new model and simulation without physical experiments?

When I read strong papers from, say, the Journal of Fluid Mechanics, a simple model, simulations and physical experimental results are given, showing good agreement. Can one publish a new model and ...
80 views

### What's a nice simple PDE to play with in Matlab?

I want to learn a very simple PDE to gain physical and mathematical intuition—a PDE with just one spatial dimension $x$ and a time dimension $t$. And, I want to write code for it in Matlab and use a ...
61 views

### Solving a 1D diffusion equation with linear and nonlinear source terms

I would like to numerically solve the following equation: $$\frac{\partial \rho (z,t)}{\partial t} = B(N_D \rho (z,t) + \rho(z,t)^2) + D \frac{\partial^2 \rho (z,t)}{\partial z^2}$$ with the boundary ...
81 views

### Modelling flow through pipe networks

I'm trying to educate myself on modelling solute flows through pipe networks. This is a follow up of my previous post here $$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$ While ...
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### Operator splitting for 4 subproblems

Typically an ODE System which involves 2 different physical problems such as diffusion and advection can be numerically approached by the well known Strang operator splitting scheme. I'm wondering if ...
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### Limit to volume change in a discretized mathematical model?

I have set up a mathematical model describing the diffusion of ozone out of a gas bubble. The bubble is surrounded by a thin gas film. So actually, the model describes the diffusion of ozone through ...
3k views

### How does one calculate reaction force in FEA?

I wrote a UEL (User Element in Abaqus) for one element and compared to a reference UEL which used standard FEM, where the results agreed satisfactorily, except the reaction force. The stress, strain, ...
154 views

### Non-linear flux interface condition - variational formulation

Context: I am working on implementing this paper and I am struggling to come up with a variational formulation for the Butler-Volmer interface conditions. To simplify my question I consider the ...
111 views

### Calculation of the EFIE integral

I need help computing the following integral: $$\int_{}\frac{(1+jk|\vec{r}-\vec{r}^\prime|)e^{-jk|\vec{r}-\vec{r}^\prime|}}{|\vec{r}-\vec{r}^\prime|}d\vec{r}^\prime$$ in this integral $\vec{r}$ ...
2k views

### Physics Simulation in C++

OK, I know a bit of C++ (very basic syntax), and I want to do physics simulation in C++, like stuff like (also the things mentioned here): Ripples and waves over a 2-d surface Vibrating string/...
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### Rotational kinematics problem @ $\theta = 0$

I'm simulating a magnetic dipole that is subjected to an evolving magnetic field. In ISO convention ($\theta$ is the polar angle and $\phi$ is the azimuthal angle), my equation of motion that is ...
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### Non-linearities in modal analysis of flexible beam

I'm trying to analyse the behaviour of a wind turbine blade rigidly connected to a wall during fatigue testing, being excited in it's first mode in two orthogaonal directions simultaneously (the first ...
98 views

### Finite-volume method applied to a particular advection equation

I'm trying to apply the finite-volume method (FVM), with which I'm not so familiar, so a simple 1D PDE equation. I already asked this question in the math stackexchange, but was told that it could be ...
200 views

### PDEPE nonlinear

I would like to use Matlab's pdepe to solve this system: $$s_t =(sr)_x + s_{ xx } \\ r_t =(\frac{ A }{ B }r^2+s)_x + \frac{ A }{ -K } r_{ xx }$$ where $A$, $B$ ...
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### Uniform distribution in 3D space [duplicate]

Posted this at math stack exchange as well, but alas no replies! So, I have been trying to find ways of distributing particles of spherical or other shape in 3D space, e.g. rectangular space. Random() ...
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### In Matlab, how can I be consistent with units?

I am modeling some aerodynamics equations and am using meters / centimeters, kilograms, and seconds. I've heard that, "matlab doesn't know units". So, how can I make sure that it does? Just ...
131 views

### Rule of thumb for time-step for solving Maxwell's Equation using 3D-FDTD?

Is there something like a rule of thumb for an adequate time-step size when solving Maxwell's equation for the interaction of light with matter? I guess a single wave oscillation has to be resolved ...
385 views

### Scaling/nondimensionalization for numerical optimization

I have a numerical optimization problem that I am trying to scale appropriately, in order to allow for the solver to achieve faster and more accurate results. I found a paper here that had a short ...
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### How to determine a PDE which is structure-preserving (energy, mass conserved)?

How to determine if a PDE is structure-preserving (energy，mass conserved)? Are there some standards in judging the preserving-structure? Or rather, how to derive the formulation of energy-preserved ...
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### Fit constant term in LM algorithm

I'm using the Levenberg-Marquardt algorithm to fit my data with a Gaussian function: $$f(x)=a\cdot e^{-\frac{(x-c)^2}{2\sigma^2}}+f_0$$ $a$, $c$, $\sigma$ and $f_0$ are the fitting parameters. The ...
148 views

### Reasons to choose LES in stead of RANS models? (turbulence)

In oceanography, is there any particular reason why choosing large eddy simulations in stead of RANS (regardless of the type of flow)? In both cases, 2d simulations would be used (shallow water model)....
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### Strange solutions using Finite Element Analysis

I've implemented the Finite Element Method to model the heat transfer between two different materials where one material is surrounded by the other. When I run the model I'm getting some strange ...