# Questions tagged [numerical-modelling]

The tag has no usage guidance.

198 questions
Filter by
Sorted by
Tagged with
74 views

1 vote
81 views

### 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 ...
• 156
1 vote
45 views

### 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 ...
• 91
8k 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, ...
194 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 ...
163 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 $\vec{r}$ ...
• 21
9k 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/...
• 121
1 vote
61 views

### 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 ...
• 217
115 views

### 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 ...
143 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 ...
285 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 $A$, $B$ ...
• 3
1 vote
23 views

### 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() ...
• 45
1 vote
362 views

265 views

### 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 ...
1 vote
234 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 ...
• 156
564 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 ...
244 views

### 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 ...
• 11
1 vote
51 views

### 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 ...
• 131
172 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)....
• 31
1 vote
117 views

### 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 ...
• 11
137 views

### If a numerical solution remains constant for different grid sizes, what does it mean?

I'm testing a finite volume scheme, Godunov type solver, using a problem with analytical solution. I'm not able to reproduce the solution, which includes source terms. I tried with different mesh ...
• 31
2k views

### How to construct an ellipsoid using Ansys design modeller (or any other 3D CAD software) [closed]

I am working on numerical simulation of breast model to evaluate the use of thermal imaging for breast cancer detection. To do this I need to construct an ellipsoid rotated 30 degrees around y-axis ...
571 views

### Discrete wave simulation - absorbing boundaries?

I wrote a simple 2D wave simulation using the following equations: $$\frac{\partial^2 u}{\partial t^2}=c^2\nabla^2u$$ Where $\nabla^2$ is the discrete laplace operator using a Von Neumann neighborhood ...
• 171
1 vote
118 views

### If I discretize a PDE in space with WENO and in time with an implicit method, do I need to solve a nonlinear algebraic system at each time step?

I am attempting to solve a nonlinear advection diffusion equation $$\frac{\partial u}{\partial t} = \frac{\partial}{\partial x}(\frac{\partial u}{\partial x} + u^2)$$ with Robin boundary conditions ...
148 views

### Good numerical method for solving the Kadomtsev Petviashvili equations. Is there an analytical solution?

I need to solve the Kadomtsev Petviashvili (KP) equations $$\partial_x(\partial_t u+u \partial_x u+\epsilon^2\partial_{xxx}u)+\lambda\partial_{yy}u=0$$ where $$\lambda=\pm 1 \;.$$ My questions ...
• 445
1k views

### 1-D incompressible unsteady Couette Flow Explicit finite differece CFD

I am currently following J.Anderson Jr.'s CFD with basic application and I came into some troubles while coding for my very first CFD problem. As the title suggests I am solving an incompressible ...
• 33
1 vote
105 views

### Declare variable to substitute one calculate only once

Frame of the question I am currently editing an add-on module to an ocean/circulation model, which is written in Fortran. The code of the main model is quite optimized with respect to short run time (...
802 views

### CFL condition in Discontinuous Galerkin schemes

I have implemented an ADER-Discontinuous Galerkin scheme for the resolution of linear systems of conservation laws of the type of $\partial_t U + A \partial_x U + B \partial_y U=0$ and observed that ...
• 173
203 views

### Chattering effect using ode23s -- SDOF with variable spring and periodic input force

I am attempting to model the following SDOF system with a variable spring and having a sinusoidal input, $$m\ddot{x}+(k_0+k_1)x = m(2\pi f)^2\sin(2\pi ft)$$ where $m$ is the mass, $k_0$ the original ...
• 133
1 vote
58 views

### elliptic equation with exponential coefficient

I'm trying to solve the following equation $$\dfrac{\partial}{\partial x}\left(e^{au}\dfrac{\partial u}{\partial x}\right) = 0$$ Of course, this equation can be solved analytically. I am trying to ...
1 vote
I am solving a first-order ODE: $\frac{\partial \rho }{\partial t} = -a \rho^2 + b |A(t)|^2 \rho +c|A(t)|^{2m}$ This is the evolution of the plasma density in the presence of a laser pulse (complex ...