For questions regarding the choice and/or appropriateness of conditions necessary to model a particular phenomenon with a partial differential equations.

learn more… | top users | synonyms

0
votes
1answer
27 views

imposing “measured data” to Dirichlet boundary conditions in fenics

I'm relatively new to fenics and I just looked through all questions related to Dirichlet boundary conditions. I don't seem to find a well-described question or answer about what I'm about to ask. I'...
1
vote
1answer
24 views

heat equation on bounded and unbounded domain

I have been reading about the heat equation and I am confused about uniqueness in the case when the domain is bounded and when it is not. In the book I am following, it is common to write the heat ...
0
votes
0answers
28 views

How to add a Ricker Wavelet (Mexican Hat) to a 2D/ 3D fem mesh?

I have a 2D square mesh and a 3D beam shaped mesh and I want to propagate a seismic wave in them. I am trying to simulate them using Open source FEM codes (fenics). I have left the top surface to be ...
1
vote
0answers
40 views

Pressure boundary condition in Navier-Stokes equations

I would like to solve 3D transient incompressible Navier-Stokes with FEM, Newton method, Schur-based preconditioner, Lagrangean P2/P1 elements (no stabilization), in a rigid pipe discretized with ...
3
votes
2answers
58 views

2D Laplace problem with mixed boundary conditions using Conjugate Gradients

I am being asked for one of my classes to solve 2D Laplace equations with mixed boundary conditions using the Conjugate Gradient method. The equations and conditions are given as: $$ \frac{\partial^...
0
votes
0answers
25 views

Solving Laplace's Equation in Cylindrical Coordinates in Mathematica

This is my first attempt at solving a PDE with boundary conditions numerically, and I'm not sure if Mathematica has that functionality built-in. Basically, I am trying to solve Laplace's equation in ...
0
votes
0answers
38 views

I'm comparing two different methods for solving the Navier Stokes equations. Why are my velocity results so different?

I just posted a question with this exact title at the "Mathematics" part of Stack Exchange and someone directed me here. Apologies if it is not OK to double-post. I want to use a code for modeling ...
1
vote
0answers
35 views

Issues with self-consistent Poisson-Schrodinger solver

I'm currently in the process of writing a self-consistent Schrodinger-Poisson solver for a device heterstructure (High Mobility Electron Transistor). The algorithm is based off of this journal(1). I ...
5
votes
1answer
48 views

Recovering pressure from velocity or streamfunction fields

I am interested in 2D channel flow of an incompressible Stokes fluid (Re = 0), with periodic boundary conditions in the x-direction and no-slip at the walls in the y-direction. I have existing code ...
3
votes
1answer
39 views

Definitiones of solid, fluid, and boundary nodes in the context of LBM

In the family of Lattice Boltzmann (LB) methods, like many others, one deals with three types of node; namely, fluid node, solid node, and boundary node. (I know; the boundary node is a subtype of ...
3
votes
2answers
165 views

Determine numerical infinity for Schrodinger equation $−\psi''(x) + x^ 2 \psi(x) = E\psi(x)$

Consider the following Schrodinger equation for the harmonic oscillator with real $x$: $$ −ψ''(x) + x^ 2 ψ(x) = Eψ(x). $$ I solve the last equation using shooting method and implicit Runge-Kutta ...
3
votes
1answer
32 views

Apply second order finite difference discretization for mixed boundary condition

I want to solve the problem below \begin{equation} \begin{aligned} \eta u-\Delta u &=f, &\text{in $\Omega$}\\ \end{aligned} \end{equation} where $\Omega=(0,1)\times (...
1
vote
1answer
97 views

Outflow boundary condition

I know that in outflow boundary we assume a zero normal gradient condition and use upwind scheme for approximation. However, I saw this sentence in a book which I do not understand; "Convective fluxes ...
0
votes
1answer
62 views

Boundary conditions generalized eigenvalue problem

Consider the following eigenvalue problem \begin{equation} \mathcal {L} x(s) = \lambda x(s), \end{equation} where \begin{equation} \mathcal {L} = \alpha \partial^4_s + (s^2-1)\partial^2_s + s \...
2
votes
1answer
123 views

How do I program periodic boundary conditions? [duplicate]

Hi I have a code below that solves non linear coupled PDE's given Dirichlet boundary conditions. However I need to implement periodic boundary conditions. The periodic boundary conditions are ...
5
votes
1answer
98 views

How can i convert a boundary flux condition into an internal source term?

Imagine a rectangular box that is thermally insulated on all sides except for one, where a heat flux is applied. Now imagine the same box with the same conditions on all sides except that the side ...
1
vote
1answer
71 views

Finite difference scheme for Webster equation

Webster equation is a popular generalization of 1D wave equation used for ducts of variable cross-section $S \equiv S(x)$. Assuming harmonicity in time, the spatial equation for propagation of ...
0
votes
0answers
41 views

Using Periodic BC for Taylor Green Vortex Flow Simulation

I want to solve the very simple case of two dimensional Taylor Green Vortex Flow. I am using incompressible Navier Stokes equations and Artificial Compressibility Method as my solver where I introduce ...
0
votes
0answers
50 views

Periodic boundary conditions for solving Navier Stokes Equations on a Staggered Grid

I want to solve two dimensional Navier Stokes equations on a staggered grid for the case of Taylor-Green Vortex. My initial conditions are standard sine and cosine functions. As I am aware, I should ...
3
votes
0answers
45 views

Reflecting boundary condition posed as a Riemann problem

I am trying to implement a solver for the Euler/Navier Stokes equations. I have a problem implementing boundary conditions for the wall. I am using an unstructured solver. A lot of literature says ...
1
vote
1answer
73 views

How to deal with PDE over the real line

I have a PDE defined over $\mathbb{R}$, for which I don't have the exact solution, and I am to approximate it with finite differences so I need to input some BC. Can anyone suggest any good ...
1
vote
1answer
154 views

Shooting method - Matlab ODE

I'm trying to solve these equations of hypersonic adiabatic flow over a flat plate. I did all the simplifications and got these equations for the stagnation point flow. $$\left(Cf''\right)' + f f'' = \...
0
votes
1answer
76 views

boundary conditions of linear advection problem

I am solving the 1D advection problem given by: $$\frac{\partial u}{\partial t}=-c\frac{\partial u}{\partial x}$$ where c is the wave speed, and u is the unknown field variable, and x and t are time ...
6
votes
1answer
180 views

Poisson equation finite-difference with pure Neumann boundary conditions

I'm trying to solve a 1D Poisson equation with pure Neumann boundary conditions. I've found many discussions of this problem, e.g. 1) Poisson equation with Neumann boundary conditions 2) Writing the ...
1
vote
1answer
125 views

Numerical method for a BVP with mixed boundary conditions (MATLAB)

I've been given a second-order non-linear ODE: $$\frac{d^{2}\theta(s)}{ds^{2}} = sf_{g}\cos{\theta} + sf_{x}\cos{\phi}\sin{\theta}$$ where $f_{g}, f_{x}$ and $\phi$ are constants. The boundary ...
1
vote
0answers
85 views

Boundary Conditions for the given PDE

I'm working on the Black-Scholes equation, but I'm pretty new to financial modeling. Right now, I am trying to understand the Black-Scholes PDE. I understand that the Black-Scholes equation is given ...
1
vote
0answers
70 views

Center of mass in systems with periodic boundary conditions

I have a question about the calculation of center of mass (COM) in systems with periodic boundary conditions. There is a method introduced here: https://en.wikipedia.org/wiki/Center_of_mass#...
0
votes
0answers
30 views

Boundary conditions shooting method

I am trying to solve the differential equation $\frac{d^{2}y}{dr^2}+(\frac{1}{r}+1)y=0$ with the boundary conditions $y(r) \rightarrow r \frac{dy}{dr}(0)$ as $r \rightarrow 0$ and $y(r) \rightarrow ...
0
votes
0answers
54 views

problem with understanding the fluid boundary conditions of a 1D probelm

I am having problems understanding the boundary conditions of the problem described in this paper on researchgate Essentially the problem consists of a one dimensional fluid chamber in contact with a ...
1
vote
2answers
151 views

BCs in a coupled problem

Consider a thermo-mechanical coupled problem, where coupling exists from both the sides, mechanical loading producing thermal effects and vice versa. In such a case, is it necessary to always ...
3
votes
2answers
139 views

Understanding Neumann BC

I understand what Neumann BC means physically and how to imply them. However, I am not able to perfectly understand it the way it is represented mathematically as $\partial u / \partial n$ where $n$ ...
0
votes
1answer
140 views

How to implement 'stress-free' boundary conditions (stokes flow)?

I have to implement 'stress-free' boundary conditions for a stokes flow of a 2D-domain (for the left, bottom and right boundaries). The boundary condition are also described mathematically as $2 \eta \...
4
votes
1answer
100 views

How to physically understand time dependent boundary conditions?

I am a beginner in Computational science and FEM. I came across some PDEs which implement time dependent boundary conditions. I am not able to visualize exactly a physical scenario of how that would ...
2
votes
1answer
85 views

Laplace's equation with periodic Dirichlet boundary conditions

Consider a Laplace's equation with Dirichlet boundary condition: ${\nabla ^2}\Phi = 0$ in a domain $D$ with given Dirichlet Boundary condition: $\Phi=\Phi_o$ at $\partial D$ (smooth, but not ...
2
votes
0answers
79 views

Finite difference aproximation - Darcy law

I am solving following problem: Filtration of water can be described in bi-dimensional case by $$- \partial_x(K(x,y) \partial_x u ) - \partial_y (K(x,y) \partial_y u ) = 0, $$ where $u$ - water ...
2
votes
0answers
101 views

Solving constrained BVP, singular Jacobian

The boundary value problem is $$ \begin{cases} \dot{x}_i = \begin{cases} (0.5D^{-1}\psi)_i, \text{ if }(0.5D^{-1}\psi)_i \le 0 \\ 0 \text{, otherwise} \end{cases} \\ \dot{\psi} = 2\Sigma x \\ x(0) =...
4
votes
0answers
145 views

Boundary conditions in the Finite Element Method at only one side of computational domain

I want to solve a Sturm-Liouville problem in 1D, i.e., \begin{align} [p(x)\ u'(x)]'+q(x)u(x) = f(x) \end{align} with boundary conditions \begin{align} u(0)=a \hspace{1cm} u'(0)=b \end{align} How do I ...
3
votes
1answer
93 views

LU-SGS and boundary conditions

I am trying to understand how boundary conditions are implemented when one uses the nonlinear LU-SGS algorithm for Euler equations. Most papers describe the Gauss-Seidel sweep over mesh cells, but do ...
3
votes
1answer
124 views

Smoothed particle hydrodynamics bounduary (ghost particles) properties

I am learning SPH method. At the moment I am trying to implement simulation described in this very good article. However I don't get how the ghost particles properties are computed: Position of the ...
2
votes
0answers
180 views

FEniCS: both normal and shear stress boundary conditions for elasticity? [closed]

I would like to have both the normal (xx) component and shear (xy) component of a 2D (stress) tensor defined on a boundary (y=const, for instance) for an equation which is of the type $$ \nabla \cdot ...
3
votes
2answers
114 views

How to implement boundary conditions in heat equation with no flux and fixed value at the same time? Is it Robyn BC?

I am modeling the temperature of the groundwater using heat equation. I have Dirichlet BC at the top but at the bottom I have constant temperature equal 12 degrees C (see attached pic). It is look ...
4
votes
2answers
167 views

FEM: Possible to have boundary conditions “inside” the domain?

I work on geological problems and I use the Finite Element Method. But this question can be applied on other classical mechanical problems. I work on implicit 3D surfaces (which represent the limits ...
5
votes
1answer
174 views

Do the class of PDEs that lack initial conditions have a name?

I am trying to think of what this kind of problem is called. I illustrate it with a telegrapher's equation with (hopefully) standard notation. Find $u:\Omega\times \mathbb{R} \to \mathbb{R}$ such ...
1
vote
2answers
196 views

Dirichlet BCs - alternative implementation methods

I am having problems with solving a hyperbolic wave problem with Dirichlet BCs. I have tried reducing the time step sizes, which does not affect the results, and notices increasing the number of nodes ...
1
vote
0answers
45 views

should boundary conditions be effecting moving mesh results?

I have a question on the use of moving mesh to solve the inviscid euler equations. I have solved the following equations: $$\frac{\partial}{\partial t}\left[\begin{array}{c} \rho\\ \rho u \end{array}\...
1
vote
0answers
53 views

Jacobi method converging then diverging

I am working to solve Poisson's equation in 2D axisymmetric cylindrical coordinates using the Jacobi method. The $L^2$ norm decreases from $\sim 10^3$ on the first iteration (I have a really bad guess)...
3
votes
0answers
391 views

What should be the number of boundary conditions of a PDE [closed]

As far as I know, for getting a unique solution to a PDE we should impose some boundary conditions to the PDE. "The number of required auxiliary conditions is determined by the highest order ...
0
votes
0answers
289 views

Finite Difference Method Neumann Boundary Condition with Variable Coefficients by Ghost Points

I have found an alternative solution to the problem stated here. Here's the alternative solution link. It says that "A common technique in implementations of $\partial u/\partial x=0$ boundary ...
2
votes
0answers
101 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 ...
3
votes
2answers
275 views

How to efficiently implement Dirichlet boundary conditions in global sparse finite element stiffnes matrices

I am wondering how Dirichlet boundary conditions in global sparse finite element matrices are actually implemented efficiently. For example lets say that our global finite element matrix was: $$K = \...