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.

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### Numerical algorithm to compute second order solution of non-linear advection with source

I would like to solve the following equation, $$\frac{\partial f}{\partial t}+\frac{\partial}{\partial x}\left({\mathcal A}f\right)=S(x,t)$$ where $f$ is a function of $x$ and $t$, ${\mathcal A}$ is a ...
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### Numerical solution of an advection equation, $\frac{\partial P}{\partial t}+\frac{\partial}{\partial x}\left(P^{5/3}\right)=0$, with finite volume

I was trying to solve the following equation numerically, $$\frac{\partial P}{\partial t}+\frac{\partial}{\partial x}\left(P^{5/3}\right)=0$$ I adopted the Godunov approach for discretising the ...
108 views

### Solving compressible euler equations in non-conservative form

I am trying to solve the following compressible 1D system of equations in two non-conservative form PDEs for $\rho, Y$ and one ODE for $v$ \begin{align} \rho_t+(v+Q)\rho_x &= -\rho q(Y,T,\rho)-...
1 vote
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### blown up solution for linear advection in upwind method with finite difference

I am going to solve this advection equation regarding the flow simulation of an energy tower \begin{equation} Y_t+ v(t) Y_x =0 \end{equation} with the following boundary conditions which depend on ...
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### 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 ...
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### 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 ...
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### WENO scheme on the advection of a fluid in a compressible porous media

I am working on reactive transport and I need to solve this advection equation: \begin{align} \frac{\partial (\phi C)}{\partial t} = - \nabla \cdot \big(\vec{q}(\phi) C\big) \end{align} with $\phi$ ...
1 vote
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### Computing Jacobian in WENO scheme for advection in a porous media

I am trying to implement an advection equation for a coupled system of a two-phase flow in a porous media using a WENO scheme . My equation is of the form: \begin{align} \frac{\partial (\phi(x,t) C(...
482 views

### WENO Scheme for 1D linear advection equation

I have been stuck for a while now on a WENO scheme implementation and I have a few questions concerning the implementation, but also the theory behind it. For context: I'm currently working on ...
1 vote
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### Semi-lagrangian method for compressible fluid (non divergence free)

I am looking for a semi-Lagrangian method for advection with a non divergence free velocity field. The equation is \begin{align} \frac{\partial C(x,t)}{\partial t} &= - \nabla \cdot (\vec{v}(x,t) ...
1 vote
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### Solving 1D Advection Equation Using Midpoint-Rule and Finite-Differences

I want to solve the advection equation ($v_0 \in \mathbb R$) $$\frac{\partial f}{\partial t} + v_0 \frac{\partial f}{\partial x} = 0$$ using 2nd order Runge Kutta like the midpoint rule for the time ...
1 vote
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1 vote
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### Attempt on 2d Advection with FDM - With Code

I tried to implement the 2d advection problem with a velocity field, that is not constant in space. My problem is, that the "mass" of my shifted density gets "eroded" or just ...
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### Global reconstruction defined elementwise in a-posteriori error estimator

This question is a follow-up of this previous one. In "Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems" by Georgoulis et al., an error estimator is ...
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### TVD Lax-Wendroff with non-constant velocity

I am dealing with a linear advection equation with a non-constant velocity, where I would like to apply a TVD Lax-Wendroff scheme in 1D. The equation is the following: \begin{equation} \frac{\...
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### Why the numerical solution of advection-dominant problem is challenging

In many CFD text books, usually there is a dedicated chapter for advection term discretization. Why discretization of such term in advection-dominated problems and near the discontinuities is ...
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### Efects from the boundary in advection equation [duplicate]

I am implementing the advection equation $u_x+(1/c)u_t=0$ following a Crank-Nicholson finite difference scheme. The equation for this is \begin{eqnarray*} -\frac{\gamma}{4} w_{n-3 j+1} + w_{n-2 j+1} ...
1 vote
I'm trying to solve this advection-diffusion equation (ADE): $$\frac{\partial \phi}{\partial t} + \nabla \cdot (-D \nabla \phi + \mathbf{u} \phi) = 0$$ In fact, this ADE framework is coupled to a ...