All Questions
32
questions
3
votes
1
answer
189
views
Numerical scheme for the level set equation that solves inverse mean curvature flow problems
I am considering the problem of simulating the evolution of an interface given as a curve in 2D (or surface in 3D) that evolves according to a velocity specified at the interface of the form:
$$\vec{v}...
- 33
3
votes
1
answer
189
views
Discontinuous Galerkin for transport equation with non-constant advection
This question is mainly an inquiry about the usefulness of Discontinuous Galerkin (DG) for the time-independent transport equation of the form
$$\sigma u+\beta\cdot\nabla u =f,\;\;\;\text{on }\Omega\...
- 139
2
votes
3
answers
178
views
Should reaction be taken into account in the CFL condition when solving advection-diffusion-reaction equations numerically?
I'm dealing with the numerical resolution of advection-diffusion-reaction equations.
I've encountered references on CFL conditions for conservation laws as well as advection-diffusion equations.
I'm ...
- 61
4
votes
3
answers
533
views
Why not use the convolution theorem for explicit timestepping?
Consider the advection equation
\begin{equation}
\frac{\partial C}{\partial t} + u\frac{\partial C}{\partial x} + v\frac{\partial C}{\partial y} = 0
\end{equation}
I want to do a forward time, center ...
- 181
1
vote
0
answers
60
views
Stability plot of upward difference implicit time
I am analyzing the stability of 1D convection (advection) equation as shown in the picture. When I derive the equations as shown I want to get rid of the complex number.
I`m asking if those stability ...
1
vote
0
answers
177
views
Integrating a wavelike equation with absorbing boundary conditions
I am trying to numerically solve the following equation:
$\frac{\partial^{2} \phi}{\partial t^{2}}-\frac{\partial^{2} \phi}{\partial x^{2}}+V(x) \phi(x, t)=0$ On some domain, with:
$\phi(x, 0) = I(x)$
...
- 111
0
votes
1
answer
301
views
Why this error occurs in my code for Lax Wendroff?
I want to implement the Lax Wendroff method for a non linear advection equation which is
$$\frac{u_{i}^{n+1}-u_{i}^{n}}{t} + \frac{f(u_{i+1}^{n})-f(u_{i-1}^{n}) }{2h} -\frac{t}{2h} \left( F_{i+1/2}^{n}...
user37062
1
vote
1
answer
707
views
What is wrong in the code for this upwind method?
I want to implement the upwind method in following advection equation problem :
$$ u_{t}+2 u_{x} =0 ,$$ for $0\leq t \leq 1,$ $0\leq x \leq 1 $
$$ u(0,x) = u_{0}(x) = \begin{cases}
10^4 (0.1-...
user37062
1
vote
1
answer
172
views
Finite Difference for Advection Equation With Source
I'm trying to find a convergent finite difference scheme for the PDE
\begin{equation}
\begin{split}
u_t + (x-1) u_x &= (x-1)u, \hspace{.5cm} x \in [0,1] \\
u(x,0) &= 1 \\
u(1,t) &= 1. \\
\...
- 141
0
votes
0
answers
84
views
numerical solution to pde on an ellipse
Looking for advice on discretization (preferably finite difference) schemes for pdes on curves in general, but in this case it is an ellipse (so given by $(a\cos(r), b\sin(r)$). The problem is the ...
- 11
1
vote
0
answers
50
views
Comparison of convection time - theoretical value vs computed
This is a follow up to my previous post here,
I'm solving for convection in 1D
$$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$
The discretization of the above equation is ...
- 433
1
vote
1
answer
856
views
Is there a general analytic solution to 1D advection of velocity, $u_t=-uu_x$?
This is to help me relate continuous and discrete, predict what my scheme should be doing, and move toward using the method of manufactured solutions.
There's a solution for constant velocity $c$ ...
- 364
2
votes
1
answer
312
views
Finite difference method not working for advection PDE with negative coefficient
I'm trying to solve a very simple advection PDE
$\frac{\partial u}{\partial t}+c\frac{\partial u}{\partial x}=0$
where $c<0$.
I have been able to implement a simple Modelica code to solve the ...
- 147
1
vote
0
answers
339
views
Crank-Nicolson scheme in space for advection equation
Consider the equation
$$\frac{\partial}{\partial t}v(t,x)=\frac{\partial}{\partial x}v(t,x)$$,
for $t,x\in\mathbb{R}$.
I'd like to solve this equation forward in space and backward in time, ...
- 133
1
vote
0
answers
320
views
Why can I not solve the negative advection equation (backwards in time)?
Suppose we have the negative, inhomogeneous advection equation:
$$\left(\frac{\partial}{\partial x}-\frac{1}{c}\frac{\partial}{\partial t}\right)v(t,x)=u(t,x)\qquad(t\in\mathbb{R}_{+},x\in\mathbb{R})$$...
- 133