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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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401 views

DIIS method to accelerate SCF convergence for stretched geometries

I am implementing from scratch an Hartree-Fock calculation in the STO-3G basis set to perform Born-Oppenheimer molecular dynamics. I have a Restricted Hartree-Fock procedure that can reproduce very ...
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49 views

Phase dislocations and numerical accuracy

I am solving the nonlinear Schrodinger equation (NLSE), $$A_t+iA_{xx}+i|A|^2A=0$$ where $A$ is a complex valued function, which can be written as $A=ae^{i\theta}$ for $a,\theta$ real. Now, for ...
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92 views

Crank-Nicolson integrator: oscillations with complex matrix

I'm working on a Real-Time TDDFT implementation and I am currently comparing different propagation schemes for the propagation of the Kohn-Sham wave function, $$ \phi(t+\Delta t) = \hat{\mathcal{U}}\...
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93 views

How can I evaluate the accuracy of my n-body simulation?

I am making an n-body simulation in python. There are many different methods to numerically solve the system of differential equations governing the gravitational interactions between the $n$ ...
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48 views

Should I expect computational gains using a second-order splitting method here?

I am trying to solve a three-dimensional baroclinic transport problem. The hydrodynamic (three-dimensional shallow water) equations are: \begin{align} \nabla \cdot \vec{v} = 0, \tag{1} \\ \frac{\...
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88 views

Non-reflecting boundary conditions for compressible Navier-Stokes equations

I have some questions about the implementation of non-reflecting OUTFLOW boundary condition for Navier Stokes equations. Following Poinsot, Lele "Boundary Conditions for Direct Simulations of ...
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64 views

Cavity Flow CFD Boundary conditions and strange waves

So I have a PDE that I use to describe how material flows through a volume(2D or 3D). $$\frac{\partial C}{\partial t} + \vec{u} \cdot \nabla C = (D' + D )\nabla^2C$$ Now using finite differences I get ...
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75 views

Numerical error in implementation of iterative algorithm

I am trying to implement (in Python for now) low thrust orbit propagation for spacecraft using universal variables. For a given central body with the gravitational parameter $\mu$ and an orbit with ...
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97 views

Journals that publish theoretical analyses of existing algorithms

In computational physics, the vast majority of papers has the following structure They propose some new algorithm, or improvement to an existing one They give numerical examples, ideally comparing ...
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158 views

Solving a 3D (almost radial) convolution with FFT

I have a 3D integral that is almost a radial convolution of the form $$ \int d^{3}k'h(\mathbf{k'})g(|\mathbf{k-k'}|) $$ and I am looking for a fast and efficient algorithm (e.g. FFT) to solve it ...
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47 views

Numerical Euler Rotation Equation

The problem I have may be really simple, but still getting a hard time solving it. So I have the Euler rotation equations: $$I_{1}\dot{\omega}_{1}+\left(I_{3}-I_{2}\right)\omega_{2}\omega_{3}=\...
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51 views

Coupled Diff Equation from Bose Einstein distribution

I am a student doing physics hons and have had very little experience in programming. This semester we are supposed to do a computational project in thermodynamics. I have to solve these two coupled ...
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90 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 ...
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588 views

Using RK2 Method to solve the simple harmonic oscillator of a horizontal mass on a spring (1D)

Being new to numerical analysis techniques, in particular RK2, I decided the best way to jump in is by using python to solve the well known mass-spring oscillator using RK2 techniques. My problem is ...
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58 views

How to model pedestrian flow through subway systems?

I'm a New Yorker and take the subways every day. I have a growing interest in understanding the distribution of paths people take on the subways to work every day. I.e. if there are $n$ subway ...
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102 views

Solving Schrodinger's Equation Numerically in a Bunimovich Stadium

I need to solve, as mentioned, Schrodinger's equation in a Bunimovich stadium-shaped infinite potential well with Dirichlet BC Numerically (this isn't possible analytically). In order to do so, I need ...
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240 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 ...
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68 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(...
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574 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\...
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176 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 ...
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0answers
128 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 ...
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141 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-...
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56 views

How to solve potential flow with FEM, stream function, and the Kutta condition?

I'm trying to solve two-dimensional potential flow over airfoils with the finite element method, using the stream function formulation ($\Delta\psi = 0$, $u = -\partial\psi/\partial y$, $v = \partial\...
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84 views

How to simulate water, falling under gravity, and impinging on a curved surface, which is kept/present in a domain, containing air?

TL;DR: How do I simulate a hole, at the bottom of a (full) water tank? I am attempting to simulate water, flowing out of a hole/slit, at the bottom of a tank (Water Domain) (under the influence of ...
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0answers
36 views

Numerically solving a system of parabolic PDEs and 1st order ODEs

I'm trying to solve the following system of differential equations numerically. What are the available finite difference approaches and matlab solvers to solve such a system? Other approaches to solve ...
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61 views

Split step Fourier method to solve Schrödinger equation for moving potential

I'm trying to use the excellent Schrodinger Python class by Jake VanderPlas (https://jakevdp.github.io/blog/2012/09/05/quantum-python/) to simulate a wave packet within a moving Gaussian potential. I ...
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213 views

Which solvers for BVP in python are the best? Is there something better that scipy.integrate.solve_bvp?

I am trying to solve a boundary value problem with Python. I have been using scipy.integrate.solve_bvp but the result that it is giving me is completely wrong. Basically my code is as follows: ...
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30 views

How to numerically transform a 2D Fourier spectrum with arbitrary frequency shift to center frequency?

Suppose $F(u,v)$ is the center frequency Fourier representation of some $f(x,y)$ in 2D. $$ f(x,y)=\int\limits_{-\infty}^{\infty}\int\limits_{-\infty}^{\infty}F(u,v)e^{2\pi i (xu+yv)}dudv $$ In ...
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0answers
75 views

Finite difference methods for coupled 2nd order nonlinear pdes

I have a system of coupled nonlinear PDEs that I cannot figure out how to solve in a smart way using FDM, so I was hoping someone here might have a clue. The equations go as: \begin{align*} \frac{1}{...
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0answers
47 views

Jacobian Elements for Coupled Drift-Diffusion System using Vertex-Centered Finite Volume

I'm trying to solve the fully coupled drift-diffusion system using Newton's Method. Although I eventually plan to potentially use a Jacobian-Free Newton-Krylov approach, this is still something that I ...
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0answers
39 views

Huge accelerations in plasma simulation

I'm trying to make a numerical simulation of pulsar magnetosphere using FDTD on a log-spherical Yee lattice for fields and PIC for plasma particles. Field part is working like charm but issue arises ...
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89 views

Band structure of nonlinear Schrodinger equation with one dimensional potential

I have a nonlinear Schrodinger equation which reads: $$ \frac{1}{2} \frac{d^2u}{dx^2}+ |u|^2u + V(x)u = -i \frac{du}{dz},$$ where $V(x)=\cos(wx)+ i a \sin(wx)$ and $w$, $a$ are numbers. How to ...
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99 views

Solving complicated coupled ODE using RK4/ODE45 in Matlab

I have the following coupled differential equations also known as Guiding Center Approximation. It is used to explain the position- and velocity change of particles (electrons and protons, N = 1000) ...
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72 views

Numerical scheme to solve Maxwell equations with fixed potential boundaries?

We have a 2D electromagnetic field (in the sense that: $E=(E_x,E_y,0)$, $B=(0,0,B_z)$, and all derivatives with respect to $z$ are $0$), and we are considering a system made up of two walls at $x=-b$ ...
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50 views

Dealing with simultaneous collisions in N-body sim

I have written an 2d N-body simulation in Python which allows collisions between the bodies. A body is modeled as a circle whose area is proportional to its mass. Each time the sim advances by one ...
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0answers
45 views

Is a noise that perturbes the system less than the algorithmic uncertainty reasonable?

I am solving a stochastic differential equation with a small noise to update the velocity of particles. Then I update their position according to an Euler scheme. I am using a step h=0.001. The ...
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336 views

One Dimensional Schrodinger's Equation solution using Numerov Method

I have been trying to solve Time Independent Schrodinger's equation in one dimension using Numerov Method as discussed in this excellent lecture notes I found on net. The Numerov method can solve an ...
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0answers
111 views

Second Quantization in Matlab

This question may be more suited for physics.stackexchange, but I saw this post was recommended for StackOverflow or Computational Science, so I'm asking my question here. I am trying to write a ...
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0answers
69 views

Finite difference scheme for unconfined aquifer equation

For an unconfined aquifer we have this PDE for the water table position( of course after somehow making the original Boussinesq equation linearized ): $$ \frac{\partial^2(h^2)}{\partial x^2} + \frac{\...
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165 views

Double Integrating acceleration data to obtain position: 2 Problems

I have a data sample from an accelerometer from my phone (pretty bad accelerometer though). I'm trying to double integrate it in order to obtain the position as a function of time. I'm using a program ...
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0answers
112 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 ...
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0answers
189 views

1d turbulent energy spectra in homogenuous direction (non-isotropic)

I am trying to compute the one-dimensional energy spectra for my channel-flow simulation. I have already written a post-processing script to achieve this, however I need to validate my code before ...
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0answers
45 views

Parallelizing molecular simulation with full configuration energy

First, let just me stress that I'm not a an expert in computation chemistry, so now the problem: We have GCMC molecular simulation, in the Grand Canonical ensemble, using the standard metropolis ...
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0answers
224 views

Physics of explosions: just vorticity?

eg 1 2. Is it just vorticity? What's actually happening? (Similar: steam engines, volcanoes, clouds). examples are grid-based, using "vorticity confinement" in Phoenix FD. EDIT Some techniques: "...
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41 views

Software suggestion for simulating the stacking of sedimenting rods

I'd like to simulate the following problem: Define some square, horizontal and hard area onto which cylinders (aspect ratio R) sediment. Preferably, the source of cylinders sequentially generates N ...
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0answers
152 views

Mass conservation in atmospheric continuity equation numerical solution

My phd project is heavily related to numerical modeling of planetary atmospheres. In particular now I am dealing with a particular expression of the continuity equation, involving a thermodynamic flux....
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0answers
59 views

Sensitivity Analysis — Total Variation for a function with categorical arguments?

I have an application in sensitivity analysis of complex system models with moderately nonlinear interactions between arguments Arguments potentially dozens or hundreds in number Arguments mostly ...
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0answers
79 views

The Schrodinger equation for time-dependent Hamiltonian after one timestep, taking exponential or use ode solver?

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ Assuming I knew $\psi(t)$, I want to know $\psi(t+\Delta t)$. Should I take exponential ...
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0answers
62 views

Metropolis algorithm and thermal sine-Gordon model

I try to simulate thermal version of 1D $(x, t)$ sine-Gordon field model. I am interested in finding thermal static solution that minimizes functional of energy $E$: $$E = \int dx \left( \frac{1}{2} \...
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0answers
80 views

How to get the eigenvalues of Hamiltonian in an over complete basis

Let $|\psi_i\rangle$, $i=1...N+m$, be a set of overcomplete basis vector in a $N$-dim Hilbert space. The following are known: (Einstein's summation convention assumed) $$\hat{H}|\psi_i\rangle=H_{ji}|\...