# Tag Info

## Hot answers tagged hyperbolic-pde

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### Why do we solve non-linearity in hyperbolic PDEs that way?

The good thing about the conservative form is that this comprises multiple models, such as Shallow Water Equations, Euler Equations or traffic models. An essential feature of hyperbolic equations is ...
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### Understanding the Courant–Friedrichs–Lewy condition

I have two extra points I would like to add to Wolfgang's answer. A formulation of the CFL condition that I find more useful than the classic formula is this: A necessary condition for the ...
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### Understanding the Courant–Friedrichs–Lewy condition

You are correct: If you satisfy the CFL condition, then all that guarantees is that your scheme is stable, i.e., the numerical solution does not go to infinity. But the CFL condition says nothing ...
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### why not all conservation laws solved numerically by hyperbolic methods

The core difference between the two PDEs you presented is that the heat equation is parabolic while Burgers equation is hyperbolic. This means that for Burgers equation changes in the solution travel ...
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### When is it safe to ignore the diffusion term in an advection-diffusion equation?

The stationary equation you show transports information from the right to the left via the advection term; it also diffuses slightly. If you switch off the diffusion term altogether, then you only ...
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### why not all conservation laws solved numerically by hyperbolic methods

Actually, the heat equation can be, and often is, solved by hyperbolic methods. Instead of writing $q=-u_x$, write $q_t=-(u_x+q)/\tau$. Instead of the heat flux becoming instantaneously equal to the ...
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### Shallow water equations (SWE): well-posed initial data for single travelling pulse

What you are looking for is known as a simple wave solution, in which the variation in the solution belongs entirely to one characteristic family. If you had a linear hyperbolic system, this would ...
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### Problems with manufactured solutions for 1D inviscid burgers' equation

You simply have a bug in your code. The flux is $\frac{1}{2} u^2$ and not $\frac{1}{4} u^2$.
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### stability of a numercial scheme for a hyperbolic system?

It is worth making some additional points. What you set out is just one version of the Lax-Wendroff method. That scheme is unique in one space dimension but has several free parameters in two or three ...
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### Numerical flux and source term in FVM (Burger's like equation)

The time evolution equation in hand is $\frac{\partial}{\partial{t}}{u} = L_1(u) + L_2(u)$ where the operators in the RHS are $L_1 = -\frac{\partial}{\partial{x}}{f(u)}$ and $L_2 = g(u)$. The ...
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