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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878 views

How to implement Newton method in solving 1D PDE system? (ie. Poisson eq, continuity eq, drift-diffusion eq.)

I want to solve PDE system, which consists of Poisson equation, continuity equations for electron and hole with drift-diffusion equation numerically, by using method called Newton's method. This ...
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1answer
40 views

Solution of Coupled Differential equation for a 2d linear flow using RK4 method in python 3

I want to study the dynamics of a 2d linear flow, whose dynamical equation is- $\begin{pmatrix} \dot{x_1}\\ \dot{x_2}\\ \end{pmatrix}=\begin{pmatrix} 1 & 1\\ 4 & -2\\ \end{pmatrix}\begin{...
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1answer
57 views

Which are the right configurations in the Markov chain of a Hamiltonian Monte Carlo algorithm?

I have a question about the Markov Chain Hamiltonian Monte Carlo (MCHMC). Hamiltonian Monte Carlo is known as Hybrid Monte Carlo too. I'll describe the steps of the algorithm. We have at the ...
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1answer
196 views

Runge-Kutta fourth order method. Integrating backwards

I am using a Runge-Kutta fourth order method to solve numerically the usual equation of motion of a background scalar field in curved spacetime with a quartic potential: $\phi^{''}=-3\left(1+\frac{H^{...
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1answer
2k views

Is there an advantage of using a staggered grid over a regular one when combined with high order methods?

The title says is all. This question is in the contest of an incompressible Navier-Stokes solver. Specifically, I am currently working on a new solver while referring myself to an older code for ...
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1answer
458 views

Implementing velocity verlet for harmonic oscillator in C gives error wrt conservation of energy

I'm attempting to implement velocity Verlet with a harmonic oscillator in C, but I have some errors: Energy is not being conserved Energy oscillates much more than I would expect I believe the error ...
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1answer
52 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...
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1answer
217 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 ...
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1answer
71 views

Applications of Julia in Chemistry and Molecular Physics?

I was wondering if there are any Theoretical & Computational Chemistry (MM, QM) codes or publications out there that are based primarily on the Julia programming language?
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1answer
219 views

What is the relationship between shape functions, interpolation functions, and degrees of freedom?

I am a newbie in FEM. I would like to get clarity regarding a few questions on shape functions in this post (please use as simple language as possible). What is the relation between Shape function ...
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1answer
269 views

Problem concerning a part of a simulation for the Ising Model

I was wondering if anyone could help me with a simulation in Python (there is a small part of the code where I have a question) about the Ising model. First, I wanted to get the magnetization $M$ ...
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2answers
78 views

Guaranteed equality between binary results with increasing MPI processes

Testing on an MPI scientific code for compressible flow dynamics I noticed that the results may depend on the number of processors used for the calculation. In fact, comparing the binary files they ...
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3k views

Solving the 1D Particle-in-a-Box using C++

I've just finished learning the physics behind the problem and would like to write a program in C++ than can solve the problem. I'm actually stuck at the start. I've quite a bit of research, the ...
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1answer
120 views

Oil/Water interface simulation using GROMACS

I would like to perform a decane/water(tip4p) interface simulation using GROMACS to analyse the fluctuation of the interface over a long period of time (50ps - 1ns). Though I have a rough idea on ...
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1answer
307 views

Higher-order Verlet integration

I'm using a simple version of Verlet integration for a particle–particle interaction system with collisions. At the end of each iteration, I integrate like this: ...
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1answer
274 views

Numerical Free Fall Analysis with RK4

I am trying to calculate real speed and time in free fall of a body. I wrote a code in Fortran and I am trying to improve it by using RK4 method x=time y=total free fall Purple line using: ...
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2answers
94 views

Should energy be conserved in an N-body simulation where particles don't lose energy in collisions?

In an N-body simulation where forces between particles are attractive and particles do not lose energy on colliding with walls or each other, should energy be conserved? How could it be, with total ...
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1answer
66 views

nodal lines of wave-function $\psi(x,y) = \sin 12x \sin y + (1 + \epsilon) \sin x \sin 12y$

I am trying to reproduce this figure of nodal lines of a wavefunction from this work of Berry $$\psi = \sin 2r\,x \sin y + (1 + \epsilon) \sin x \sin 2r\,y$$ Here the image. The first is $\epsilon = ...
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1answer
107 views

What is a good algorithm, and framework, to calculate centres of gravity or mass (cog)?

I'd like to take an photograph, subdivide it into a tesselation, either of squares, or (ideally), hexagons, and then find the centre of gravity (or, if you prefer, centre of mass) of each cell of the ...
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1answer
135 views

Boundary treatment with higher order methods

I wrote a code which solves the 2D Poisson equation with homogeneous Dirichlet BC everywhere and a source term of -1. I am using the classical Jacobi iteration method. The grid is $N_x \, \mathrm{x} \,...
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2answers
106 views

Definition of inflow boundary in CFD

If $w$ is the vector of conservative variables, $f=f(w)$ the flux function, I think have read somewhere (I can not find it anymore) that the inflow boundary $\Sigma$_ is characterized by: $\Sigma_{-}...
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2answers
93 views

Propagation of error using Euler's first order method [duplicate]

I was estimating a falling object's position versus time by using a simple first order step function, where ...
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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 ...
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1answer
57 views

How long should the hyperelastic equations be solved before updating the mesh?

How long should the hyperelastic equations be solved before updating the mesh? To be specific, I'm interested in the hyperelastic model with a neo-Hookean solid: $$ \nabla\cdot\sigma + f = \rho\ddot{...
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1answer
99 views

Operator splitting to solve time dependent Schrödinger equation

I encountered the split operator method to solve the time dependent Schrödinger equation during a lecture. I understand the method on a theoretical basis (I think at least), but I'm struggling to ...
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1answer
169 views

For a determined (known) Space charge density, what are the conditions to obtain the Electric potential/field distribution? (COMSOL, MATLAB)

Theoretic part From the theory, in Electrostatics inside a real dielectric material between real conductors, in a simple 1D plane geometry between points $P1$ and $P2$, according to the current ...
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1answer
78 views

Manual for library Libxc

Where can I find the manual for software library Libxc for exchange-correlation functionals? Links with domain www.tddft.org don't work.
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1answer
55 views

Should the derivative of an array be calculated array by array or element by element in CFD codes?

I am making my own finite difference computational magnetohydrodynamic code in Fortran 90. Looking at other codes they appear to calculate for example their $x$-derivatives, bb of their variables, e.g....
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1answer
82 views

Loss of energy when using Roe Solver for solving onedimensional Shallow Water Equations

I have written a Roe solver with Harten entropy fix code in Matlab to numerically solve the one-dimensional Shallow Water Equations. : \begin{eqnarray} \dfrac{\partial h(x,t)}{\partial t} + \dfrac{\...
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1answer
525 views

Can we simulate rigid body motion using finite element analysis?

I was wondering if we could model rigid body motion of bodies using finite element models. Particularly I'm interested to know if we can model motion of objects with no constraints or with some ...
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1answer
74 views

Defining dimensionless tempearture for Periodic flow systems

Given a flow inside a square duct with constant temperature at the walls $(T_{w1} = T_{w2} = T_w)$ the physical property in terms of temperature that repeats itself in a periodic fashion is the $\...
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1answer
688 views

Proper boundary conditions for potential flow around cylinder

I am computing the stationary, incompressible, inviscid and irrotational flow around a circular cylinder using a discretization in general coordinates. I derived a PDE and proper boundary conditions ...
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2answers
173 views

Discussing the energy spectrum of Langevin Dynamics simulation of many atoms

UPDATED I've coded a multiparticle MD simulation in 3D. It is based on Langevin Dynamics, with random impulse and dissipation. I think the program works correctly now? I have attached the plots of ...
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2answers
157 views

Computational Physics: Finding the Diffusion Coefficient from the Discretized Diffusion Equation

I'm pretty new to translating simulation to reality so please forgive the perhaps naive approach I'm taking here. If we have a (quasi-2D) experimental video of a certain concentration changing with ...
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1answer
117 views

Finding the lowest $n$ eigenvalues of a band-diagonal Matrix

I have a real sparse matrix of the form $$ \left( \begin{array}{ccc} h_{11} & h_{12} & 0 & h_{14} & & & \\ h_{21} & h_{22} & h_{23} & 0 & h_{25} & & ...
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1answer
414 views

Difficult bug in my 2D Compressible Euler solver

For the past few days, I have been writing a numerical solver for the 2D compressible Euler equations for an ideal gas. My numerical method has been the Local Lax Friedrichs or "Rusanov's method." ...
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1answer
137 views

How to determine the truncation error with products and quotients

If I have an equation given by $$\displaystyle Y = \frac{a^2}{d^2}\frac{(1-c^2\frac{c}{a})}{(1-b^2)}$$ and I expand $a,b,c,d$ in a Taylor series, where $a$ is truncated at the $A^{th}$ order, $b$ is ...
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1answer
81 views

Convergence Criteria for Two Fluid Flow Solver

Which one of the following is suitable for judging convergence in Two-Fluid Flow Solver? 1) Absolute Residual (L^2-Norm). 2) Relative Residual. 3) Fraction Change in Velocity, Pressure and Volume ...
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1answer
275 views

Solving a linear system whose matrix has imbalanced diagonal entries

I am trying to solve following set of equations: A(i,i-2)*u(i-2) + A(i,i-1)*u(i-1) + (A(i,i)+β(i) )*u(i) + A(i,i+1)*u(i+1) + A(i,i+2)*u(i+2)= B(i) + β(i) where i=1:1000000 If values of β varies(...
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1answer
98 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 ...
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1answer
152 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 ...
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1answer
182 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. ...
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1answer
559 views

How does Abaqus calculate Hill's function for non-rectangular coordinate systems?

Within the manual, the effective/von Mises stress or Hill's potential for anisotropic bodies is calculated in Abaqus in cartesian rectangular coordinates as $\sigma_{eff}=\sqrt{I_{1}^{2}-3I_{2}} \\ f(...
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1answer
92 views

Trouble Making 3rd-Order Sympletic Integrator for Planitary N-Body Problem (A Hamiltonian System)

I am doing a solar-system simulation. I am using Ruth's 3rd order sympletic integrator to avoid the problem of Energy Drift (which I had with RK4), but the the planets quickly leave orbit, and energy ...
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0answers
54 views

Problems with simulation of a spatial filter 4f setup (Python)

I have a question about my code which computes numerically the output field of a 4f setup with a pinhole in the middle which works as a spatial filter. My setup consists of two lenses with 50mm focal ...
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78 views

More efficient way to calculate magnetic field using Biot-Savart

I am writing a program in python that is supposed to calculate the magnetic field along a conducting coil that is made up of a bunch of points, and the magnetic field is generated by other conducting ...
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52 views

Lattice spring models vs. finite element models

I am a beginning graduate student in the field of continuum mechanics. It is my understanding that most problems in this field are numerically solved via finite element methods (FEM). However, I have ...
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29 views

Tackling multiscale problem in numerical simulation

In a dusty plasma system there are more than one component with different masses, i.e, electrons, ions,neutrals and dust grains. Accordingly, there are more than one temporal and spatial scales ...
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1answer
105 views

Numerical integration methods: Explicit vs Semi-Implicit vs Newton-Euler 1, 2 and use in cyclone physics engine

I am trying to understand the difference between explicit Euler and semi-implicit Euler integration, where in explicit Euler the current position is calculated as $$x_{n+1} = x_n + v_n$$ and semi-...
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58 views

Radial Hartree and exchange-correlation potentials

According to [1] the one-dimensional Kohn-Sham equation is given by $$ \left( -\frac{1}{2} \frac{d^2}{dr^2} + \frac{l(l+1)}{2r^2} + V[\rho;r]\right) rR_{nl}(r) = \varepsilon_{nl} rR_{nl}(r) $$ where $$...

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