Hi,
I work in the area of multiphase modeling and encountered the following problem.
I want to use weno algorithm on the projected characteristic variables of the problem, as follows
W(i)=inverse(P(i+1/2)) V(i)
The estimation of P is done via arithmetic average or roe's averaging of V(i) and V(i+1) where V is the primitive vector, W is the characteristic vector and P is the diagonalization matrix of the corresponding jacobian matrix of the system.
However, the cell value of the characteristic have the following structure: the same value for all the cells except on cell which has a different value. This structure of the data is obtained for the shock tube problem (and some other problems as well). If I try to implement weno on this kind of data pattern, eventually spurious oscillation would be emerged.
Summarizing s the problem: W(i)=1 for all “i” except for one cell which has value other than one.
For the one-phase problem, the data pattern of the characteristic values is different and therefore this problem does not exist. Trying implementing weno on conservative or primitive variables, results in oscillations as well
Is it possible to circumvent this problem somehow? should I think of other ways to obtain high order spacial accuracy without weno knowing this data structure of characteristic variavles?
Dear Sir:
a) SIMPLE algorithm is used more for steady-state problem
http://www.cfd-online.com/Wiki/SIMPLE_algorithm
b) PISO algorithm is more for unsteady analysis, depend of your investigations, that is the case of unsteady partial cavitation problems.
http://openfoamwiki.net/index.php/PISO7
good luck
Hi,
I worked on shock tube problem last year during my Master's thesis but it was for single phase. I did not get significant oscillations even when I applied weno scheme for conservative variables. Are you using higher order time stepping like RK along with weno?
The problem is not in the time stepping. The problem arises due to the eigenvectors and their data pattern for two phase flow.
Hi Ory,
In case of two or more fluids the problem of spurious oscillations is common for standard shock-capturing schemes which have been successfully used for single phase flows. You can find the oscillation free implementation of WENO scheme for two-phase case in the paper of Johnsen and Colonius "Implementation of WENO schemes in compressible multicomponent flow problems" J.Comp.Phys. v.219, 2006.
If you have more questions please let me know.
Best,
Andrey
Hi,
Thank you all for the replies,
Two-phase models are non-conservative in their nature, therefore the implementation as in Titarev&Toro is not suitable.
In Colonius 2014 paper, the mixture model (five equations) was presented where there are only one density and pressure variables.
For the seven equations model, the characteristic variables has the following form:
W_1= rho_g - P_g/c_g^2
W_2= P_g - \rho_g c_g u_g
W_3= P_g + \rho_g c_g u_g
and three more variables with the subscript "l" for the liquid phase.
where c_g is the gas speed sound, \rho_g -gas density, p_g- pressure density.
Eventually the data pattern for the stencils around the discontinuity for the shock-tube problem (see "A Multiphase Godunov Method for Compressible
Multifluid and Multiphase Flows" Saurel and Abgrall 1999), is :
i-2 | i-1 | i | i+1 | i+2
14.28 |14.28 | 49.99 |14.28 |14.28 |
For all the other grid stencils the values is 14.28
Applying WENO-5 where the convex combination incorporates three stencils would eventually results in the emergence of spurious oscillations, for this data pattern, even after the first iteration.
There is some information missing which, I think, could be important. First, which equations are you solving? Multi-component Euler, I suppose, but with viscosity? And finally, which kind of flux splitting do you use?
Dear Sir:
a) SIMPLE algorithm is used more for steady-state problem
http://www.cfd-online.com/Wiki/SIMPLE_algorithm
b) PISO algorithm is more for unsteady analysis, depend of your investigations, that is the case of unsteady partial cavitation problems.
http://openfoamwiki.net/index.php/PISO7
good luck
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