All Questions
Tagged with finite-difference matlab
71
questions
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1D FDTD simulation of plane wave propagation and the Courant stability condition
I'm currently trying to simulate a simple case of wave propagation in free space before adding in more complexities, and already I'm stumped. I understand the Courant stability condition. However, I ...
- 1
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53
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Prof A. Stanoyevitch's finite difference based PDE matlab code
Where can one find Prof A. Stanoyevitch's finite difference based PDE matlab code? They have a book on such a topic but can't find the accompanying code.
Is it well received? It's not commonly talked ...
- 317
3
votes
1
answer
391
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Generalized eigenvalue problem for large, potentially ill-conditioned systems
Say that I have a generalized eigenvalue problem of the form $$Ax=\lambda Bx.$$ Using MATLAB, some naive ways that one may solve this is by either
directly inverting $B$ then applying the ...
- 43
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Need help implementing finite difference Beam Propagation Method to Solve 2-D Helmholtz equation
I am trying to implement beam propagtion method in a two-dimensional lattice to solve Helmholtz equation by following the scheme given this paper. I am using Matlab for implementation.
The expected ...
- 11
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81
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Best approach to solve this system of equations?
I have the following 1D (in space, that is) system of equations I would like to solve:
\begin{equation}
\rho_{fs}\frac{\partial x_{fs}}{\partial t} = h_m\left(W_a - W_{fs}\right) - D_{eff}\left(\...
- 9
2
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1
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579
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Numerical solution of 2D wave equation using Fourier transform and finite differences
This is the $2$-dimensional wave equation
$$ u_{tt} = u_{xx} + u_{yy} $$
with initial condition $u(x,y,0)=f(x,y)$ and $u_{t}(x,y,0) = 0$.
The inverse Fourier transform used is
$$ u(x,y,t) = \iint \hat{...
- 121
-1
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1
answer
154
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The local and average Nusselt number in a square cavity
I am in the process of programming the local & average Nusselt number in a left vertical wall but my Matlab script gives me inappropriate values and it doesn't change with changing of Rayleigh ...
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2
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2
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100
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Possible to use Iterative FD methods to solve a transformed non square domain [matlab]?
For the 2-D Poisson equation $$-(u_{xx}+u_{yy}) = f \ \ \text{where} f = 1$$
For boundary conditions
$$\frac{\partial u}{\partial n} = 0 \ \text{on AB and AD}$$
$$ u = 0 \ \ \ \text{on BC and CD no-...
- 23
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votes
1
answer
145
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Time & Space matlab discretization Finite Differences confusion
I have been trying to solve this equation and write the finite difference scheme in matlab for months, but I still am not successful.
Given the KdV Equation $$\tag{1}u_{t} -6uu_x+u_{xxx}=0$$
I have ...
- 23
3
votes
1
answer
142
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Mineral dissolution and solute transport around a solid
I am trying to simulate solute transport of acid (HCl) and consequent mineral dissolution around a grain (calcite).
The governing equation for transport is the advection-diffusion equation, given as:
...
- 55
2
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0
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122
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Solute transport around a solid obstacle
I am a newbie in CFD and single/multiphase flow and transport in general. As part of my quest to learn, I am trying to model solute transport around a solid object in the center of a 2D domain. The ...
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1
vote
2
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192
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Continuation of solution to $-\nabla\cdot (k(x,y)\nabla u)=f$
I'm trying to solve the following problem, I had previously opened another discussion for the implementation and well, it seems that it has turned out well, it can be found here.
I need to calculate ...
- 123
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2
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429
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Implementing routine for $-\nabla\cdot (k(x,y) \nabla u)=f$ in Matlab
I am solving the Poisson Equation for 2D given by the following expression:
$$-\nabla\cdot (k(x,y) \nabla u)=f$$ in a rectangle with Dirichlet conditions on the boundary using Matlab.
In principle I ...
- 123
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76
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How to solve this boundary value problem which has more unknown than equation on MATLAB
I need your helps about solving the problem below with MATLAB. I am trying to solve 2D Stress Wave Propagation problem by using FDTD(Finite difference time domain) method on the cylindrical coord. I ...
- 21
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450
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Verification of order of convergence of Implicit Euler Method to numerically solve Black-Scholes PDE
I'm trying to verify the order of convergence for implicit Euler method to numerically solve Black-Scholes PDE. Theory says that it should be $O(\Delta t + \Delta S^2).$ My code is working absolutely ...
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