# Questions tagged [numerical-modelling]

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96 questions
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### 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 ...
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### ODEs vs DAE vs ADE?

I am totally confused between ODEs which I am familiar with, and differential algebraic equations (DAE) and Algebraic Differential Equations (ADE). Are they the same but just different names or what ...
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### What are the differences between CFD simulations and realistic ocean/atmosphere model simulations?

The field of computational fluid dynamics (CFD) is dedicated to solving the Navier-Stokes equations (or some simplification of them). A subset of CFD, ocean and atmospheric models numerically solve ...
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### 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 ...
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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 ...
168 views

### A simple PDE solution question

I need to ask a question about partial derivatives. I want to solve this equation (steady state, one dimensional continuity equation): $$\frac{\partial (\rho u)}{\partial z}=0$$ which is equivalent to:...
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### 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 ...
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### Very simple (real) experiment for computational methods class

I am in the process of collecting material for a class in computational methods. It will include introductions into numerical methods for ordinary differential equations (Runge-Kutta methods, multi-...
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### Numerical solution of Geodesic differential equations with Python

I have made a solver based on the SymPy.diffgeom library, where I use Scipy.Integrate to solve the following system of second order differential equations : \begin{align} u'' &+ \Gamma^0_{00}(u')...
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### 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 ...
634 views

### A Question About the Rhie-Chow Interpolation Used for Solving the Incompressible Navier-Stokes Equations on Unstructured Grids

When using the SIMPLE method on a mesh with a collocated variable arrangement, the following interpolation is used for the advecting velocities: u_f = \overline{u}_f - \overline{D}_f\...
108 views

### Is a divide by zero error an indication of a bad conceptual model?

When we create numerical models of a real-world system, we usually go through a few phases (from Abramowitz 2010): a perceptual model, where we consider the relevant components of the system a ...
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### Return derivative vector from odeint scipy function

I have the following function that I want to implement in scipy.integrate.odeint ...
984 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, ...
100 views

### How to discretize the surface of a prolate spheroid?

I need to discretize the surface of prolate spheroid given by the equation $$\frac{x^2}{L^2} + \frac{y^2}{D^2} + \frac{z^2}{D^2} = \frac{1}{4}$$ The surface has to be divided to 500 equal panels to ...
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### 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 (...
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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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### Implementation of 1D Advection in Python using WENO and ENO schemes [closed]

I'm trying to implement 1D advection solver using WENO and ENO schemes. $$\frac{\partial u}{\partial t} + \frac{\partial f(u)}{\partial x} =0$$ where: \begin{...
129 views

### Libraries to deal with unstructured grids

I am dealing with a *.cgns file. This mesh format, when saved as an unstructured grid, holds nodes coordinates, nodes connectivity per element and boundary ...