Questions tagged [advection]

To move in some direction (as a fluid does in a pipe). Often contrasted with diffusion, which is a spreading out without necessarily having any movement of the field as a whole.

Filter by
Sorted by
Tagged with
0
votes
1answer
551 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 ...
0
votes
1answer
550 views

Find cfl condition

We have the advection equation $u_t+a u_x=0, a>0, 0<t<T_f, x \in \mathbb{R}$ with initial condition $u(0,x)=u_0(x)$. Suppose that we have the following sheme: I want to find the CFL ...
4
votes
2answers
1k views

Advection equation using the finite element method

I want to solve this simple advection equation using the finite element method. $$\frac{dc}{dt}+v\cdot\nabla c = f$$ What's the best FEM discretization for this? I have tried using the standard/...
3
votes
2answers
153 views

what do zero real parts of eigenvalues mean? Any good references?

I am solving a 1D advection problem of the the form $$dQ/dt=[A]Q$$ where {Q} is the vector of unknowns and [A] is the matrix of coefficients of spatial discretisation. I have worked out the ...
2
votes
0answers
150 views

what do positive real parts of eigenvalues mean?

I am solving a 1D advection problem of the the form $$d{Q}/dt = [A]{Q}$$ where {Q} is the vector of unknowns and [A] is the matrix of coefficients of spatial discretisation. I have worked out the ...
2
votes
0answers
119 views

Calculating theoretical order of accuracy of least squares fit advection scheme

I'm familiar with finding the order of accuracy using von Neumann analysis for finite difference schemes formulated using Taylor series expansions. But is there a similar technique for finding the ...
2
votes
1answer
3k views

Implementation of 1D Advection in Python using WENO and ENO schemes [closed]

I'm trying to implement 1D advection solver using WENO and ENO schemes. \begin{equation} \frac{\partial u}{\partial t} + \frac{\partial f(u)}{\partial x} =0 \end{equation} where: \begin{...
1
vote
1answer
242 views

CFD: Doubt with time convergence in advection fully implicit upwind scheme

I'm trying to solve an advection - convection problem using an implicit upwind scheme - you can see here the finite difference discretization used. I start the model (built from scratch on Scilab) ...
4
votes
2answers
649 views

Usability of upwind finite difference schemes

NOTE: I asked this on Mathematics Stack Exchange and there were no answers. So, I thought I might try here. Upwind schemes like the classic "upstream" scheme, can be used to solve, for example, the ...
4
votes
1answer
260 views

How to calculate numerical dispersion relations for Spectral Elements?

How can we determine the numerical dispersion relation of a Spectral Element Method which leads to coupled systems of algebraic equations? What approaches to do analysis of dispersion relations is ...
2
votes
2answers
582 views

Can the conservative form of the advection equation be re-written by replacing the velocity term with an integral over all other points in space?

Suppose I have a 1D advection equation in conservation (divergence) form $\partial_t u(x,t) = -\partial_x [v(x)u(x,t)],$ where $u$ is a conserved quantity in space, and $v$ gives the velocity of the ...
6
votes
2answers
5k views

How can I prove numerical diffusion in upwind scheme for transport equation

I was just implementing the upwind scheme for a linear transport equation $u_t + cu_x = 0$ where $c=0.5$ and I saw that the solution was indeed advected but over time it starts to diffuse. Can anyone ...
3
votes
1answer
4k views

Finite differences scheme for 2D advection equation

I'm trying to study with a finite difference method the 2D advection equation with a space-dependant flow. Taking a function $f(x,y,t)$ solution of the equation : $$ \partial_t\,f+\nabla(\textbf{v}\,...
5
votes
2answers
985 views

Advice on numerical solution for 2D hyperbolic PDE with zero flux boundary conditions

I would like to numerically solve a hyperbolic PDE of the form $\frac{\partial\theta_t}{\partial t}(x,y)+\frac{\partial\left[\theta_t \gamma_t^x\right]}{\partial x}(x,y)+\frac{\partial\left[\theta_t \...
0
votes
0answers
230 views

advection diffusion equation

Would you know what is the condition for stability for the advection-diffusion equation where we treat the diffusion part using Crank-Nicholson and the advection part using FCTS (forward in time ...
7
votes
1answer
277 views

Implementation of convection scheme given by normalized variable diagram

In finite difference and finite volume methods, convection schemes (upwind, central, quick, ...) are usually shown in a normalized variable diagram. The diagram gives the normalized face variable as a ...
3
votes
2answers
209 views

Finite Differencing of a Strange Advection-Reaction Problem

comp! I'm trying to solve the advection-reaction problem $ dg/dt = dg/dx + x\cdot g \qquad on~~x \in \Omega = (-\infty, +\infty)$ supplemented with the boundary conditions $ \lim_{\lvert x \rvert \...
6
votes
2answers
560 views

Simulating advection over a network of 1D pipes

I am trying to create a simulation to help visualize how different chemical components flow through a network of pipes with associated valves, pumps, and chemical inputs. In this simulation, the pipes ...
8
votes
2answers
13k views

How to discretize the advection equation using the Crank-Nicolson method?

The advection equation needs to be discretized in order to be used for the Crank-Nicolson method. Can someone show me how to do that?
7
votes
1answer
674 views

Conservative finite-difference expression for the advection equation

Following on from the earlier question I am trying to derive a finite-difference scheme for the advection equation which is conservative. It was suggested that for advection equation with variable ...
4
votes
1answer
109 views

Is stabilization of energy equation needed when momentum equation needs it?

When SUPG/PSPG stabilization is added to momentum equation of flow problem, is needed stabilization for energy equation also? I would guess that when stabilization for velocity works fine so one gets ...
14
votes
1answer
1k views

Can the advection equation with variable velocity be conservative?

I am trying to understand the advection equation with variable velocity coefficient a bit better. In particular I don't understand how the equation can be conservative. The advection equation, $$ \...
7
votes
2answers
325 views

Stabilization of convection-dominated flow and turbulence modeling

Are stabilization techniques for convection-dominated flows like SUPG+PSPG, interior penalty methods, etc. able to handle turbulent flows without tubulence model being employed, at least up to some ...
5
votes
2answers
807 views

Are the drift-diffusion equations from semiconductor physics analogous to solving an advection-diffusion problem?

I am trying to understand an extra terms that appears when I derive the drift-diffusion equations for semiconductors. The extra term (see below) comes from applying the chain rule to the advection ...
6
votes
3answers
3k views

Open boundary conditions with the advection-diffusion equation

Following on from my previous equation I'm would like to apply open boundary condition to the advection-diffusion equation (with reaction term), $$ \frac{\partial \phi}{\partial t} = \frac{\partial}{\...
28
votes
1answer
6k views

Conservation of a physical quantity when using Neumann boundary conditions applied to the advection-diffusion equation

I don't understand the different behaviour of the advection-diffusion equation when I apply different boundary conditions. My motivation is the simulation of a real physical quantity (particle density)...
33
votes
2answers
5k views

Strange oscillation when solving the advection equation by finite-difference with fully closed Neumann boundary conditions (reflection at boundaries)

I am trying to solving the advection equation but have a strange oscillation appearing in the solution when the wave reflects from the boundaries. If anybody has seen this artefact before I would be ...
28
votes
2answers
5k views

Is Crank-Nicolson a stable discretization scheme for Reaction-Diffusion-Advection (convection) equation?

I am not very familiar with the common discretization schemes for PDEs. I know that Crank-Nicolson is popular scheme for discretizing the diffusion equation. Is also a good choice for the advection ...
4
votes
1answer
555 views

code for surface advection (e.g. level set advection)

I have a 2D surface in 3D that I want to advect under a velocity field. More precisely, I have a surface $S$ and a velocity field $v$ and I want to advect $S$ under $v$ using the flow map of $v$, i.e....
1
vote
0answers
511 views

How to solve advection equation using semi-lagrangian method?

I am working on something that involves solving an advection equation $\partial{x}/\partial{t}+\vec{u}\cdot\nabla{x}=0$ in 3D. I discretized the space into 3d cartesian grid and used the Semi-...
14
votes
4answers
8k views

Boundary conditions for the advection equation discretized by a finite difference method

I am trying to find some resources to help explain how to choose boundary conditions when using finite difference methods to solve PDEs. The books and notes which I currently have access to all say ...
9
votes
5answers
799 views

How can I derive a bound on the spurious oscillations in the numerical solution of the 1D advection equation?

Suppose I had the following periodic 1D advection problem: $\frac{\partial u}{\partial t} + c\frac{\partial u}{\partial x} = 0$ in $\Omega=[0,1]$ $u(0,t)=u(1,t)$ $u(x,0)=g(x)$ where $g(x)$ has a ...
15
votes
2answers
7k views

Implicit finite difference schemes for advection equation

There are numerous FD schemes for the advection equation $\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}=0$ discuss in the web. For instance here: http://farside.ph.utexas.edu/teaching/...

1
2