Questions tagged [computational-physics]

Computational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists.

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6
votes
2answers
3k views

Calculating the log-determinant of a large sparse matrix

I need to calculate $\log(\det (\mathbf M_i))$ where the $\mathbf M_i$'s are large sparse matrices, which are real, symmetric and positive semi-definite. I hope to have between $10$ and $100$ of ...
2
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0answers
262 views

Implementation of no-slip boundary conditions in lattice Boltzmann method fluid simulation

My faculty advisor recommended that I take a look at the lattice Boltzmann method as an introduction to scientific computing and potentially an undergraduate honors thesis topic. I cooked up a some ...
2
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1answer
317 views

I need to scale variables to solve a 2D PDE. What are the physical considerations of scaling?

I am solving a boundary value problem in 2D via an implicit finite difference scheme. Unfortunately, although the problem is well-posed and should have a unique solution, the condition number of the ...
2
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0answers
69 views

Method for calculating the stopping distance using only integers

I am trying to find how much an engine would turn until it stops accelerating with an acceleration of $a = A \sin^2(x)$. Acceleration Integrating the acceleration I get velocity $v = A(x/2 - \sin(...
3
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1answer
272 views

Finite Difference Beam Propagation Method problem

I am trying to implement the finite difference beam propagation method to study the propagation of a TE light signal through a waveguide. However, my solutions are exponentially growing, and display ...
1
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0answers
74 views

fixed point iteration to find out second order non-linear diff equations

I am working on some model analysis, getting two diff equations and after I convert them into matrix form, I have equations looks like $$ [A][X]=C\times\big(\exp([B][X])-1\big), $$ where $C$ is a ...
3
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2answers
128 views

Boundary conditions for solving Poisson's Equation with Experimental Data

I want to numerically (with Matlab) solve Poisson's equation : $ \frac{\partial^2u}{\partial x^2} + \frac{\partial^2u}{\partial y^2} = f(x,y)$ On a rectangular domain using experimental data. From ...
3
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1answer
113 views

Solve implicit ODE numerically in orbit simulation

I'm trying to plot the orbit of a compact binary star system where general relativistic effects become important. I'm using post-Newtonian approximation and I want to solve the orbit numerically based ...
5
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1answer
390 views

H(curl) conforming Nédélec-Elements to satisfy div(B)=0

Most authors are very clear that it's very dangerous to just use $\mathrm{H}(curl)$ conforming edge elements, which are divergence free, to satisfy $\mathrm{div}(\mathbf{B})=0$ and implement this ...
6
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1answer
6k views

How do I generate Maxwell-Boltzmann variates using a uniform distribution random number generator?

I am doing a molecular dynamics simulation. I need to assign initial velocities to the atoms. I want to assign the initial velocities which follow the Maxwell-Boltzmann distribution. How do I ...
0
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1answer
105 views

How many sample points are needed when re-constructing linear combination of 2D polynomials defined over unit circle?

I have a set of first 25 Zernike polynomials. Below are shown few in Cartesin co-ordinate system. z2 = 2*x z3 = 2*y z4 = sqrt(3)*(2*x^2+2*y^2-1) : : ...
3
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1answer
974 views

Computer Build for Scientific Computing

I am currently a .NET software developer(SQL Server, ASP.NET, C#, MVC & Web Forms). In my spare time I'm researching different areas of environmental science. E.g.(Hydrology, Ecology, Atmospheric ...
2
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0answers
651 views

Precession of Mercury Python simulation

I was trying to simulate the precession of Mercury based on the perturbed solution: $$\frac{1}{r}=\frac{m}{B^{2}}(1+e\cos\phi+3\frac{m^{2}}{B^{2}}(1+e\phi \sin\phi +e^{2}(\frac{1}{2}-\frac{1}{6}\cos2\...
1
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0answers
104 views

Conservation at grid interface in adaptive mesh refinement

I am using adaptive mesh refinement to solve one dimensional inviscid Burgers equation. However I am facing some difficulty to handle grid interfaces which are not uniform (coarse-fine grid interface)....
3
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2answers
1k views

GPU-enabled Lattice Boltzmann solvers?

Is anybody aware of any GPU-enabled Lattice Boltzmann solvers (preferably on C++/OpenCL and open-source) that would be recommended? I have found Advanced Simulation Library, but it seems to be very ...
0
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0answers
107 views

How to keep velocities in check in molecular dynamics simulation?

I am trying to make a very simple molecular dynamics simulator with Reflective Boundary Conditions. I am assigning the initial positions in a cube randomly while making sure they are not too close to ...
3
votes
1answer
574 views

How can I make velocity verlet algorithm more stable?

The answer to this question implies that reducing the time step would make it more stable. However I have tried reducing the time step but the system is still unstable(the total energy increases to a ...
1
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0answers
607 views

radially averaged power spectrum of a binary image does not look like power law

It has been known that Fourier power spectrum somehow obeys power law therefore the slope of the spectrum can be used to calculate the fractal dimension of an image. Many people have used it for ...
5
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2answers
716 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: \begin{equation} u_f = \overline{u}_f - \overline{D}_f\...
2
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0answers
193 views

Modeling simple laser induced population transfer via adiabatic passage in python

I'm trying to model adiabatic passage between two levels in a three-level atom interacting with two laser fields using Scipy and Numpy.. I'm not sure if my model is wrong due to my incorrectly ...
0
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1answer
81 views

Mechanics - Rotational Inertia

I am facing a problem solving a mechanical system which is shown in the scheme below. We assume that coupling of the two shafts is done with a clutch Equations: $$J1*\frac{d\omega1}{dt} + Td(\...
3
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1answer
78 views

Is there any numerical application whose performance heavily depends on the division operation?

I am an undergraduate student majoring in computer science. Recently, I am interested in the division operation, which is not directly supported by some architectures. While some architectures ...
1
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0answers
283 views

Spin-spin correlation functions in the Ising Model Monte Carlo [closed]

I'm using the Metropolis algorithm for 2D up to 5D for the Ising Model and I want to compute the spin-spin correlation function. $$c(r)=<s_is_r>−〈s_i〉〈s_r 〉$$ but I'm not sure how to estimate $...
0
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1answer
118 views

Solving differential equations in MAPLE (ballistic curve problem) [closed]

TASK: Make a simple animation of an object shot from a catapult. Object is moving through a medium. The problem must be solved in MAPLE. NARROWING OF THE PROBLEM: 2D problem consider atmospheric ...
4
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2answers
542 views

Manufactured solution for pressure based 3d incompressible Navier-Stokes solver with wall boundaries

I already successfully verified my solver (SIMPLE-type FVM-method) with the following manufactured solution (3d Taylor-Green vortex) on the solution domain $[-1,1]^3$ with Dirichlet boundary ...
2
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0answers
129 views

Arbitrary Choosing of the Solution Domain - Navier Stokes and Manufactured Solutions

I want to verify a finite-volume solver (SIMPLE-Algorithm) for the incompressible Navier-Stokes equations by using a manufactured solution. I use Dirichlet boundary conditions for the velocity at all ...
4
votes
1answer
373 views

Is solving Verlet constraints parallelizable?

I am a computer science student and I came across the Verlet Cloth simulation. An implementation is here. I was interested in how such computation would lend itself to parallelization. The problem ...
3
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0answers
92 views

Tracking the speed of 2D oscillations on a lattice

I wrote a Monte Carlo simulation of the 2D Lotka-Volterra model on a discrete lattice (with periodic boundary conditions). A video that I produced (which images the system after some number of monte ...
0
votes
1answer
69 views

Unexpected behavior, values tend to converge instead of fluctuate. (MD)

I am writing a molecular dynamics program to create an lattice and populate it with atoms/molecules. These then are given random velocities and the system is initialized. Then throughout time the ...
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0answers
634 views

Can you provide me with the source code of DMRG writen by C++?

I want to study the Density matrix renormalization Group(DMRG). Can some one provide me with the souce code which is writen by C++ for study purpose only? The code is not necessiary very professional, ...
0
votes
1answer
137 views

MAX-SAT and MAX-cut

I have been using MAX-SAT solver to obtain the exact ground state of ising spin glass model: For 1D periodic model, for systems with 50 binary variables and interaction range of 15th nearest ...
1
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0answers
299 views

Two Dimensional Nozzle Flow

I've been looking at the book "Computational Fluid Dynamics - The Basics With Applications", by John D. Anderson, and his solution for the one-dimensional subsonic-supersonic nozzle flow using the ...
2
votes
1answer
97 views

Adjusting Keplerian orbits for thrust with numerical stability

I'm writing a mod for a game that models orbital physics (Kerbal Space Program, or KSP). I'm attempting to model the effects of thrust on spacecraft in certain states where the game only models them ...
1
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1answer
95 views

How to calculate collision force with no future knowledge

For a personal project, I am attempting to write a fairly realistic collision simulator (for relatively large objects, not quantum stuff). As I was consulting my physics textbook and various online ...
7
votes
1answer
262 views

Why should I renormalize physical variables?

I am working with legacy physical codes and I develop new ones based on the output of them. They all use their own internal normalization of variables (for example all distances are divided by the ...
1
vote
1answer
51 views

Modifying finite difference solution to Schrodinger eqn to account for fermion/boson effects

I have been playing with an implementation of Visscher's explicit method for solving the time dependent Schrodinger equation (Are there simple ways to numerically solve the time-dependent Schö...
10
votes
3answers
1k views

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 ...
2
votes
2answers
599 views

(Fortran) Integrating/summing over complicated 3D domain

I have some function $F(k_x,k_y,k_z)$ that I wish to numerically integrate over a polygon domain - physically, I am integrating over the first Brillouin Zone (BZ) of the FCC lattice (a truncated ...
0
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2answers
157 views

General question about Computational Science

I'm student of computer science (BS) and considering computational science as the field to major in for MS program. I have two questions which might look silly but I'm really confused: 1- Are ...
2
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2answers
2k views

Patankar's algorithms for Numerical Heat Transfer and Fluid Flow

I am looking for the algorithm of Patankar (for example, SIMPLE, SIMPLER, SIMPLEC and PISO) written in Fortran for the simulation of heat transfer and fluid flow.
6
votes
1answer
1k views

How to get proper parameters of SPH simulation?

I'm implementing basic fluid flow simulator using SPH method basing on e.g. https://www10.informatik.uni-erlangen.de/Publications/Theses/2010/Staubach_BA10.pdf. EDIT (dead url): https://www10.cs.fau....
0
votes
2answers
3k views

Most efficient library to diagonalize exactly large hermitian or unitary matrices

I am working on a physics problem which requires obtaining the exact eigenvalues and eigenvectors of Hermitian and Unitary matrices numerically. Naturally I would like to ask the experts what are the ...
1
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1answer
51 views

Anisotropic invariant expansion

I am trying to calculate the second and third invariants for a turbulent flow. I have the second order statistics (both transient and averaged). i.e $uu$, $vv$, $ww$, $uv$, $vw$ and $uw$. These are ...
1
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0answers
44 views

Understanding the use of Minimum Translation Vector (MTV) for an elastic collision response

So, I'm trying to simulate polygon rigid body physics, both linear and angular. To calculate the MTV is easy in SAT (Minimum Translation Vector), and to use it to adjust position is also easy: ...
4
votes
1answer
408 views

Transform from constrained to unconstrained optimization

In a constrained optimization problem, I found in a paper a way to define new variables such that the constraints disappear. They only give the new variable definitions, and I would like to understand ...
0
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1answer
68 views

Particle Collision to Static paticles

I have a system of particles with equal distance with each other and another at random positions which is moving with time. I want to know: a) The method by which I can reduce the number of particles ...
1
vote
1answer
212 views

Coupled PDE: a confusion in boundary condition setup

I have a coupled PDE problem(Poisson-Schrondinger system), i.e. first I need to solve an eigenvalue problem (Schrodinger problem discretized by Galerkin method) $$Ax=\lambda x, ~~~A=A(u)$$ the ...
1
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1answer
151 views

Trigonometric equation (Lagrange) for the double pendulum [closed]

I want to model a fishing rod and received a suggestion. I therefore try to follow the mathematics (Lagrange) of the double pendulum. I do not understand how to proceed in the step that Wikipedia ...
1
vote
1answer
167 views

Is it possible to simulate fluid dynamics in a time-based and deterministic manner?

The Problem Domain I have a number of network-connected PCs. I want to be able to simulate and replicate the same simple fluid dynamics simulation (E.g. Navier-Stokes), in real-time, between them. ...
2
votes
0answers
146 views

Why does my Finite Difference approximation not work?

I am trying to find out the magnitude of the acceleration of my object based on non-uniformly sampled 3D position data. I'm using the standard approximation of the 2nd order derivative on a non-...