Questions tagged [numerical-modelling]

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Accurately solving system of differential equations

So I am trying to solve two equations simultaneously. The goal is to find values for $\frac{de}{dt}$ and $\frac{d}{dt}$ which are the rates of change of the variables $a$ and $e$. I am then ...
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-2 votes
0 answers
22 views

How can I generate time series band-limited white noise for a given give voltage-amplitude distribution over desired frequency band in Python?

...
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3 votes
0 answers
61 views

Generalized Eigenvalue Problem using MATLAB

I'm trying to solve a generalized eigenvalue problem. I have two matrices $H$ and $S$ such that: $$ HX=λSX $$ I need to find the eigenvalues $\lambda$. The matrices $H$ and $S$ are real, asymmetric, ...
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1 vote
1 answer
110 views

What does the Chebyshev differentiation matrix look like for third and fourth derivative?

I have a PDE that contains both the 3rd derivative and 4th derivative. Example shown below $$ \frac{\partial u}{\partial t} =\frac{\partial}{\partial x}(u^3\frac{\partial^3u}{\partial x^3}) $$ $$ \...
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2 votes
1 answer
94 views

Numerical diagonalization of Hamiltonian

Framework I am trying to diagonalize the Bogoliubov-de Gennes Hamiltonian. The problem is that the Hamiltonian contains a Laplacian. This could be solved by using a discretized Laplacian. How I tried ...
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Nondimensionalization of a multi-component chemical diffusion equation

Edit I've modified the equations because they were wrong and I added the whole system, as asked by @Wolfgang I am trying to nondimensionalize a system of partial differential equations similar to 2nd ...
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3 votes
0 answers
56 views

Change in Variables applied to biharmonic equation

Background I want to solve the following biharmonic equation: $$\frac{ \partial^4 s }{ {\partial \xi}^4 }+\frac{ \partial^4 s }{ {\partial \xi}^2{\partial t}^2 }+\frac{ \partial^4 s }{ {\partial t}^4 }...
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1 answer
120 views

Can I use periodic boundary conditions for `U` but not for `p`?

Cross-posted from Stack Overflow. (https://stackoverflow.com/questions/70686368/can-i-use-periodic-boundary-conditions-for-u-but-not-for-p) I am trying to numerically compute the drag force around a ...
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3 votes
1 answer
76 views

How to model the dynamic impact of transport on boxes containing vials?

Let's consider that we have large number of boxes being transported in a truck. These boxes contain certain number of vials which in turn contain some other products. Now one would like to simulate ...
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1 answer
129 views

Solving ODE with Spectral Method using Chebyshev Polynomials

I would like to solve following the basic equation of linear elasticity (for simplicity in 1D) $$ \frac{d}{dx} \left( E \frac{du}{dx} \right) = 0 \quad \textrm{with} \quad u(1)=0, \; u(-1)=b $$ ...
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Is a 2021 MacBook Air sufficient for modeling and simulations research in fluid dynamics?

I code mostly in Matlab, simulating various simple fluid dynamics models. One particular simulation has the potential to become sort of complex, though I believe the set of coupled equations will ...
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2 votes
1 answer
115 views

Mineral dissolution and solute transport around a solid

I am trying to simulate solute transport of acid (HCl) and consequent mineral dissolution around a grain (calcite). The governing equation for transport is the advection-diffusion equation, given as: ...
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3 votes
1 answer
113 views

Solving and Plotting Mutualism Model in Python

I am a beginner in programming. I need to program a mutualism model of two species in python that would solve and graph using the following equations: $$ \frac{dN_1}{dt} = N_1(r_1 - e_1N_1 + \alpha _{...
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2 votes
2 answers
136 views

What is the most suitable numerical approach for modelling multiphase flow with particle interactions?

If I want to build a solver for this following problem: 1. There is stagnant water governed by the Navier-Stokes equation in the domain. ...
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2 votes
0 answers
72 views

Solute transport around a solid obstacle

I am a newbie in CFD and single/multiphase flow and transport in general. As part of my quest to learn, I am trying to model solute transport around a solid object in the center of a 2D domain. The ...
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2 votes
0 answers
112 views

Floquet theory for periodic delay differential equations: current numerical routines

I would like to determine the stability of a system of periodic delay differential equations (a seasonal host-parasite model). I've tried to implement the method described in Lemma 2.5 in this paper: ...
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1 vote
1 answer
85 views

Discrete model of cell - cell communication

I am trying to understand how cell to cell communication is studied using a discrete modelling framework. Could someone please suggest suitable references or libraries which already have ...
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2 votes
1 answer
69 views

Finite element modelling of thermal expansion of 3D solid bodies

I want to solve the thermal expansion of solid by using FEM approach. When I developed the model based on the the principle the minimum potential energy, the solutions for thermal expansion are not ...
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1 vote
0 answers
19 views

How can this attempt to implement a Milstein numerical approximation for an Ito process of multiple components be fixed?

I have been reading Kloeden and Platen's Numerical Solution of Stochastic Differential Equations, and have more or less been trying to systematically complete the various exercises therein as I go ...
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4 votes
0 answers
80 views

Identifying an unknown P.D.E. from solution data

I have a black-box simulation that produces the time evolution of a probability density function p(x, t) in 1 dimension from arbitrary initial conditions p(x, 0). The underlying simulation occurs on a ...
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1 answer
73 views

Does the leap-frog algorithm conserve energy for n-body problems?

The leap-frog algorithm is able to conserve to a certain extent the energy of a system, which flucutates as a cosine around a stable value. Is this true if we apply the algorithm to a n-body ...
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1 vote
0 answers
39 views

Procedure to convert continuous equations of motion to discrete version

Let's take a mobile robot and suppose we know its continuous equations of motion, for example this car-like simple model. Now if I am simulating this robot in a continuous 2D plane, then coding the ...
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0 votes
0 answers
55 views

Discretizing Multi-species Ion Exchange Equations by Finite Volume Method

I'm solving a system of multispecies ion exchange equations (diffusion+drift fluxes) in 1-d spherical domain using finite volume method to obtain the ion concentrations at the next time step. After ...
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2 votes
1 answer
115 views

How to couple the vibro-acoustic equations by Mortar method for non-matching meshes?

Assume we have two domains $\Omega_a$ a acoustic domain with boundary $\Gamma_a$ and $\Omega_s$ a domain of a solid body with boundary $\Gamma_s$. $\Omega_a$ and $\Omega_s$ have the common interface $\...
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2 votes
0 answers
63 views

Does the time-dependent 1D advection-diffusion with point sources have an analytical solution?

I am looking for the analytical solution of 1-dimensional advection-diffusion equation with several point sources, Q, along the axial length of a cylinder through which the fluid flow occurs. Neumann ...
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2 votes
2 answers
387 views

How to implement point source or volume source in finite element implementations

I'm trying to do a simple implementation to study the advection-diffusion-reaction dynamics in a straight pipe. I have points positioned along the length of the pipe (blue dots in the image above). I ...
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0 votes
2 answers
372 views

Implementing routine for $-\nabla\cdot (k(x,y) \nabla u)=f$ in Matlab

I am solving the Poisson Equation for 2D given by the following expression: $$-\nabla\cdot (k(x,y) \nabla u)=f$$ in a rectangle with Dirichlet conditions on the boundary using Matlab. In principle I ...
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How to distinguish primary hosts (stars) and orbiting satellites (planets) and tertiary bodies (moons) by their mass and trajectory?

I posted this question in the astronomy stackexchange. There are no responses, and it was suggested that I pose the question here. The "too long, didn't read" was taken from a comment, and ...
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5 votes
2 answers
590 views

Specifying ode solver options to speed up compute time

I'm specifying the 'JPattern', sparsity_pattern in the ode options to speed up the compute time of my actual system. I am sharing a sample code below to show how I ...
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1 answer
84 views

How error scales with numerical precision in molecular dynamics?

In terms of time-step, numerical error in molecular dynamics scales with square, i.e. $error \approx dt^2$. But how it look for numerical precision ? E.g. how much bigger will be numerical error when ...
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0 votes
1 answer
59 views

finding boundary conditions when transforming a higher order ode to system of first order ode

given the following ODE: $$\frac{d^{4}w}{dx^{4}} + B\frac{d^{2}w}{dx^{2}} = 1$$ with boundary conditions $w(0) =0 , w(1) = 0,w'(0) = 0,w'(1) = 0$ its possible to solve analytically but I am attempting ...
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2 votes
2 answers
171 views

Generating particles from a distribution function using Monte Carlo

I have been given a 4D ($x, y, v_x, v_y$) distribution function, $f(x,y,v_x, v_y)$, generated by an external code. I want to generate a set of particles from this distribution function, say 10k ...
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-2 votes
1 answer
64 views

Solving differential equation by setting vectorization `on` in MATLAB

This is a follow up to my previous question posted here. I've set up an ode system in MATLAB and I'm trying to vectorize the code to increase the speed of computation. The follow is the code for my ...
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0 votes
0 answers
38 views

What is an integrated modelling tool?

In this document they describe their code as an integrated modelling tool. I am trying to understand how this is different from a regular modelling tool? Most codes include different modules that do ...
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0 votes
1 answer
118 views

Solving differential equation by specifying jacobian pattern

This is a follow up to my previous question posted here I'm trying to construct the sparsity pattern of the jacobian matrix to speed up the computation of a large system of odes. The following is the ...
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1 vote
1 answer
60 views

solving differential equations with jacobian pattern

I'm trying to compare the simulation time for solving a system of differential equations with and without jacobian pattern for a toy model using ode15s in MATLAB. ...
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0 votes
1 answer
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Acoustic Simulation, how are boundaries handled?

I don't have a background in numerical modeling so this question is rather broad. What I am interested in is modeling the propagation of an ultrasonic acoustic wave in 3d space. The basic 3d wave ...
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4 votes
2 answers
165 views

Obstacle too thin in fluid-structure interaction, so I consider it as membrane

I need to simulate a 3D fluid-structure problem where the obstacle is an elastic and very thin structure (then I want to consider this structure as a surface). I need to solve this problem using ...
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6 votes
0 answers
107 views

A Question About a Claim from 1991 Computational EM paper about the Cancellation of certain Boundary Terms

Please let me know if this is not the appropriate site for this question. I found questions regarding EFIE/MFIE/CFIE on this site, so I thought my question might fit. I am studying the paper by Putnam ...
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0 votes
0 answers
49 views

Unsteady Stokes equations in ALE framework

I'm trying to solve Unsteady Stokes equations on a moving domain, using an ALE formulation, that is $$\frac{\partial \mathbf{u}}{\partial t} - \mathbf{w}\cdot \nabla\mathbf{u} = \nu\Delta\mathbf{u} - \...
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1 vote
2 answers
616 views

How to set up the differential equation system to speed up computation?

I've set up a system of differential equations, obtained after discretizing pde, in the following way ...
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  • 581
3 votes
1 answer
199 views

Choosing an appropriate time step for a discrete & continuous dynamics simulation

I have inherited of a flight dynamics simulation in C++ which represents a small drone with it's autopilot, actuator dynamics and a solid state IMU. Hence, it is composed of a few models, some ...
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3 votes
1 answer
316 views

Dirichlet Boundary Condition finite difference method using sparse-matrix $Ax = b$ system

I am trying to solve the boundary value problem for heat equation: $$ u_{xx} + u_{yy} = f(x,y) $$ where the solution $u(x,y) \in [0,1] \times [0,1]$ and the Dirichlet boundary condition $u(x,y) = ...
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6 votes
2 answers
138 views

What makes a good computational grid?

Most computational methods for solving PDEs are grid-based. What makes a computational grid "good", other than being sufficiently fine to resolve features of numerical solutions? Are grids ...
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1 vote
0 answers
91 views

How can I practice multivariable root-finding?

Recently, I've been reading up on various root-finding / optimization algorithms such as the Levenberg-Marquardt method, Gauss-Newton, Conjugate Gradient, trust-region and trust-region-dogleg. I've ...
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2 votes
2 answers
61 views

In a dynamical system, what might be a good reason why periodicity in an object's velocities is important?

I'm studying periodic motions in a dynamical system and, as a newbie, I narrowly think of an object's periodicity in its spatial x-y coordinates, but what might be a good reason why the existence of ...
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1 vote
1 answer
85 views

Would modeling a fluid flow that decreases in magnitude violate conservation of mass?

If I make a quasi-steady assumption in a model such as keeping the fluid density constant and assuming the flow is incompressible, does modeling a flow with decreasing velocity / magnitude, say, as ...
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0 votes
0 answers
66 views

The error in SOR algorithm suddenly falls to zero when it reaches 1e-7 range

I am solving the Poisson equation for heterojunction using Fortran90. I use the SOR algorithm to arrive at the potential profile. I see the weird behavior where the error (the difference between the $...
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1 vote
1 answer
593 views

Reading VTK file into C++ for analysis

I apologize in advance if this post is at all ignorant or elementary, I am a pure mathematician who is newly getting into the world of scientific computing. For my research, my advisor would like me ...
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2 votes
0 answers
54 views

Solving Stokes Equations in 3D - Do I need to treat pressure-velocity coupling iteratively?

I need to develop a code to solve Stokes Equations in 3D in cubic geometries (structured grid, uniform mesh spacing). My code needs to take a pressure gradient in one direction as a BC (pinlet=p1, ...
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