[bananaliks]

Hello,
I’m developing a finite volume code to solve 2D reacting compressible flows, but i’m getting some instabilities. The code compute the convective fluxes with a hybrid HLL-HLLC solver and diffusive fluxes with a second order scheme. The code uses a symmetric Strang splitting operator, so the solution in time t + dt is given by

U(t+dt) = C_x(t+dt/2) C_y(t+dt/2) D(t+dt/2) R(t+dt) D(t+dt/2) C_y(t+dt/2) C_x(t+dt/2) U(t)

Whre C_x and C_y are the convective operators in x and y, D is the diffuse operator and R is the reaction operator. The reaction step uses LSODA solver to solve the stiff ODE system and update temperature and mass fractions and the convection/diffusion steps uses a explicit third order Runge-Kutta method to uptdate conservative variables. To compute the convection fluxes, was implemented a fith order WENO reconstruction and a MLP5 MUSCL (Multi-dimensional Limiting Process) to get the faces values. I’m trying to simulate a flame propagation of hydrogen/air in a closed duct, but i’m getting oscillations in the interface of flame, as seen from the density plots in

Does anybody have idea why this is happening?
I'm thinking this problem is being caused by the interpolation schemes.
Thanks

[naffrancois]

Hello,

This looks like Richtmyer-Meshkov instabilities. There are shock waves which travel back and forth thoughout the contact discontinuity and this amplifies the instability.

The instability is initially triggered by your initial condition and mesh, you would not observe this if the flow velocity was perfectly orthogonal to the grid (like 1D flow configuration along the x-axis)

These instabilities can be dampened by numerical or physical diffusion. I guess here numerical diffusion is low because of your high order spatial scheme. You do not say what is your diffusion term.

So what you observe is not necessarily bad !

[bananaliks]

Originally Posted by naffrancois

Hello,

This looks like Richtmyer-Meshkov instabilities. There are shock waves which travel back and forth thoughout the contact discontinuity and this amplifies the instability.

The instability is initially triggered by your initial condition and mesh, you would not observe this if the flow velocity was perfectly orthogonal to the grid (like 1D flow configuration along the x-axis)

These instabilities can be dampened by numerical or physical diffusion. I guess here numerical diffusion is low because of your high order spatial scheme. You do not say what is your diffusion term.

So what you observe is not necessarily bad !

Yes, this like Richtmyer-Meshkov instabilities! Thanks! I will try to add some artifial viscosity.