ODE solver with WENO scheme (weighted essential non-oscillatory)

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Berry 2022-8-2

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https://ww2.mathworks.cn/matlabcentral/answers/1772770-ode-solver-with-weno-scheme-weighted-essential-non-oscillatory

评论： Berry 2022-8-3

Hey everyone,

this is rather a very specific question:

I want to solve a bunch of DAE in Matlab using ode-solver (ode15s in my case for stiff problems).

The system depends in time t and location z.

For that, I had to transform the PDAE into an DAE by discretizing in z-direction.

First I used the upwind scheme for disretization, but had the problem of artifical oscillations. So I tried to implement the WENO scheme, which is described here: meatballbw.ps (nd.edu)

After implemeting the WENO scheme, I even faced more oscillation.

Is anyone familiar with the WENO scheme or has another approach, how to solve artifical oscillation with ODE solvers. I also tried to implement a non-constant Jacobi matrix but it failed: ODE15s with non-constant Jacobian - (mathworks.com) .

Thank you for your help.

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Torsten 2022-8-3

I thought, that using first order upwind with high discretization numbers is a high order scheme, which can cause artifical ocsillation...

No. Also if you use many grid points (I think this is what you mean by "high discretization numbers"), a first-order scheme remains a first-order scheme. It will not cause artificial oscillations.

If you don't choose enough grid points, a first-order scheme tends to smear out sharp gradients. This is meant by the technical term that they "cause numerical dispersion".

Berry 2022-8-3