# Questions tagged [finite-difference]

Referring to the discretization of derivatives by Finite differences, and its applications to numerical solutions of partial differential equations.

553 questions
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### Solving numerically a linearized system of elliptic (?) Navier-Stokes equation (Shallow Water Derived)

For my PhD Thesis, my advisor asked me to build a solver inspired from the article "Optimal Control Theory Applied to an Objective Analysis of a Tidal Current Mapping by HF Radar, J-L Devenon, 1989". ...
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### Closed boundary conditions in finite difference method for diffusive-advective equation

I am implementing a finite difference method in solving the diffusive-advective equation: $$u_t + v \cdot u_x = D\cdot u_{xx}$$ (v, D are constants). Planning to use the operator splitting method (...
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### Neumann boundary condition FD implementation for instationnary diffusion equation

I am trying to solve this diffusion equation : $\dfrac{\partial D\dfrac{\partial f}{\partial x}}{\partial x}+S = \dfrac{\partial f}{\partial t}$ ($D$ is not constant and varies according to $x$) with ...
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### Finite differenced eigenvalue prob. of inhomogeneous boundary conditions?

I am basically asking about eigenvalue problems of differential equations using some finite difference method (FDM). Usually the system is subject to some boundary conditions (BC), e.g., Dirichlet or ...
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### Should ghost cells/nodes be coupled?

This is more of a theoretical question regarding the concept of ghost cells. When handling Neumann boundary conditions, ghost cells (in FVM) or nodes (in FD) are typically introduced. Essentially, ...
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### Applying Neumann boundaries to Crank-Nicolson solution in python

Consider the heat equation $$u_t = \kappa u_{xx}$$ with boundary conditions of $$u(x,0)=0\\ u(0,t)=100\\ u(l,t)=0$$ Numerical analysis by pyton can be done with ...
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### finite differences on a slanted grid — advection diffusion equation

I used pretty much all my expertise with finite differences to solve an advection-diffusion equation with space-dependent coefficient with a grid in the $x$,$z$ domain with regular spacings. Something ...
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### Numerical Lax-Wendroff scheme order of convergence on Burgers equation

I was suggested to move that question here. The question to be as follows. Statement of the problem Is it possible to achieve the second order of convergence (OOC) of Lax-Wendroff (LxW) scheme ...
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### Problems with deriving an equation for a finite-difference scheme given in the journal paper

I'm reading this paper and trying to follow everything that the author has done. A Comparative Study of Finite Volume Method and Finite Difference Method for Convection-Diffusion Problem But there ...
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### Convergence rate assesment in space/time

I am solving a hyperbolic PDE (e.g. the shallow water equations) which depends upon $x$ and $t$. Typically, the overall convergence rate is calculated by comparing the numerical error in different ...
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### Finite difference time domain and dynamic permittivity

Since the permittivity of any material is usually complex function of temperature, frequency, density, etc. I was wondering if it is possible to use a dynamic permittivity which changes as a function ...
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### Unphysical Behaviour Characteristic-Wise WENO5-Z

I am currently working on a scheme that uses finite differences WENO5-Z with 3rd Order Runge-Kutta time integration for solving the Euler equations. The code projects the conserved variables and ...
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### Finite difference method for the electric field of the electron gun

Can anybody help me to find books or MATLAB code examples for solving electric field of the electron gun(fig.1)with finite difference method? Python code examples are also perfect. The electron gun ...
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### Finite difference for computing gradients at face in finite volume code

I am working on a 3-D problem using the finite volume method (FVM). I came across a problem dealing with the computation of gradients at a face. The geometry that I'm working with is discretized ...
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### finite difference for a second order ode

I saw in a code for discretization of something like $\frac{d^2T(x)}{d^2x}$ , ( $x = sin(\theta)$ ) tries ...
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### Is there a simple way to avoid carbuncles for FD WENO methods?

I have implemented finite-difference WENO scheme for Euler equations (with some variants - WENO-JS, WENO-Z, WENO-M, different flux splitting). It works well, but have problem with so-called carbuncles ...
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### Neumann-Neumann boundary intersection

I am trying to solve a Vertex Centered, Finite Difference, Poisson equation $-\nabla^{2}u=f$ with Dirichlet boundaries on the left and bottom and Neumann boundaries on the top and right using ...
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### 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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### How to force potential boundary conditions in the Yee scheme for solving Maxwell's equations?

Assume that 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 that we are considering a system made up of two ...
I've got a data set of points $M_O .. M_N$ for time points $t_0 .. t_N$, where $N$ is approximately 10-20, and the spacing of time is not uniform (i.e., $t_{i+1}-t_i$ is not constant for all i). It is ...
As described in this Wikipedia article, a discrete laplacian matrix can be made for a 3D regular grid using Kronecker products. I'd like to use the same methodology for $(n-1)\times n$ matrices of the ...