[emjay]

Hello community.

i'm thinking about time accurate discretisation.

I know the basics about Forward Euler / Backward Euler / Crank Nicolson / BDF / RK2 and higher order / DIRK etc and how expensive some of the schemes are.

Also about the concept of TVD.

If a solution contain a discontinuity and i need preserving monoticity the requirements for spatial and time discretisation must have TVD scheme. (e.g. Superbee for spatial and RK3-TVD for time)

But how is it if the equations are elliptic, (subsonic) or the system of Equations contain an additional transport equation (e.g. concentration C). Is it necessary that this equation have also a spatial TVD scheme?

IMHO if the mesh is not fine enough unphysical oszilations would appear in the transport equations.

The goal is a higher order discretisation of the equations in time and space to avoid unphysical solution.

[FMDenaro]

Originally Posted by emjay

Hello community.

i'm thinking about time accurate discretisation.

I know the basics about Forward Euler / Backward Euler / Crank Nicolson / BDF / RK2 and higher order / DIRK etc and how expensive some of the schemes are.

Also about the concept of TVD.

If a solution contain a discontinuity and i need preserving monoticity the requirements for spatial and time discretisation must have TVD scheme. (e.g. Superbee for spatial and RK3-TVD for time)

But how is it if the equations are elliptic, (subsonic) or the system of Equations contain an additional transport equation (e.g. concentration C). Is it necessary that this equation have also a spatial TVD scheme?

IMHO if the mesh is not fine enough unphysical oszilations would appear in the transport equations.

The goal is a higher order discretisation of the equations in time and space to avoid unphysical solution.

- Provided that the BCs are regular, elliptic equations has a regular solution.

- The passive transport of a concentration C is like solving the Lagrangian equation for the particles having a constant concentration, therefore no new unphysical extrema must be generated. But the equation for such transport is hyperbolic and some flux limiter must be introduced.