# Tagged Questions

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

22 views

### Stability analysis for a hyperbolic PDE on staggered grid

I am trying to understand the stability of a finite difference equation on the staggered grid. I could understand the Von Neumann stability analysis for the collocated grid for a simple acoustic ...
64 views

### Best practice for dealing with Dirichlet boundary conditions in finite-difference schemes: add artificial unknowns?

I know of at least two ways of dealing with Dirichlet boundary conditions in finite-difference schemes (and, to a lesser extent, finite-element schemes). Here I'm thinking of solving Poisson's ...
45 views

### Can I model laminar incompressible fluid flow and heat transfer in MATLAB's PDE toolbox?

I have a system of PDEs in cylindrical coordinates that needs to be solved: 1. Continuity equation 2. Incompressible Navier stokes ( in r & z coordinates) 3. Heat transfer equation with both ...
23 views

### nonlinear coupled pde by finite difference

I want to solve nonlinear coupled PDE by finite difference method. I have done the discretization. the number of variables and number of equations are not same. How to deal with this situation?
42 views

### Oscillations in Chorin's method due to the BC

I am pretty new to the CFD and I wanted to start with Chorin's projection. The starting problem is just a free jet flowing in the investigated area. I got terrible oscillations almost immediately and ...
36 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 ...
51 views

### Heat Equation in 3D mass Matrix set-up

I am solving a 3D heat transfer equation with variable boundaries (insulated, convective, radiative or free) using a F.D.M. technique. My geometry of choice is a cube. The purpose of my work is to get ...
87 views

50 views

### Collocated Grid Navier Stokes Solver

I want to solve Navier Stokes equations on a collocated grid. Earlier, I was using a MacCormick scheme based solver where I discretized predictor step in forward differences and corrector step in ...
54 views

### How to set the temperature at the vertices points for a rectangular domain?

Suppose I have to solve the 2-D heat equation in a rectangular domain using the finite difference method, for the boundary conditions say: $T_1$ is the temperature of the right side of the rectangle, ...
133 views

### Three body problem in C++

I am in a begginers programming course and we got a little project. I chose to simulate the three body problem using the Euler method. Even though the system is chaotic there are some special cases ...
101 views

### Second order interpolation scheme

On a grid I am having the values of a physical quantity say for example Temperature, at the E,W,N,S and P node all of them being calculated using a second order discretization scheme. I want a second ...
51 views

### Gauss-Seidel iteration weighted by change

In general, I can use Gauss-Seidel iteration for finite difference solution of partial differential equations. In my case I am only solving an analog of steady-state heat transfer, so there is no ...
120 views

### How to define residual in multigrid approach?

I wish to solve the two-dimensional Navier Stokes equations using multigrid method on a collocated grid using the Predictor-Corrector method mentioned below. But first, let me elaborate on what I had ...
116 views

### Discretize Poisson equation with derivative of delta function as source

Consider the PDE $$\frac{d^2}{dx^2} g(x) = \frac{d}{dx} \delta(x-x_0),$$ with $x, x_0 \in [0,1]$ and $g(0)=g(1)=0$. What is the best method to discretise the derivative of ...
117 views

### Unwanted Oscillation in FDM simulation of elastic wave equation

I am using staggered grid FDTD for solving elastic wave equation. A description of which can be found at (geodynamics.usc.edu/~becker/teaching/557/reading/Virieux1987.pdf). I have generated a ...
125 views

### Is this finite difference approach correct?

I am solving incompressible 2D Navier-Stokes equations with zero y-component velocity. The geometry is a simple 2D pipe of a length $L$ and diameter $W$ and there is only two boundary conditions: ...
100 views

86 views

### Stability in discretization of a PDE

Suppose I want to numerically solve for $f(x,k)$ the one-dimensional Boltzmann equation for electrons in steady-state condition, given as: \left( \dfrac{\hbar k}{m} \right) \dfrac{\...