Hello,

I work on a finite volume throughflow where the inviscid effect of the blade are introduced by mean of source terms. These source terms are computed so the flow follows the camberline.

I experience problems at the leading edge (generation of entropy) because source terms are applied just downstream ot the leading edge and are zero just upstream and there is no lenght scale for this sudden application of force. Is it a numerical or a "physical" singularity ? I mean, is it a problem of my blade model or may I resolve this by a modification of my flux to take account of my source terms ?

Hope to have been clear

I have not understood your method but I have generally observed that spurious entropy generation occurs mainy at the leading edge. This could be because

(1) the grid is not fine enough in the LE region (2) your boundary condition is very dissipative.

I had the second problem in my meshless scheme (which is not a finite volume method), see the following file

http://aero.iisc.ernet.in/~praveen/papers/nwbc.pdf

The following paper which studies spurious entropy production for various wall bc might be useful to you.

Balakrishnan N and Fernandez G (1998): "Wall Boundary Conditions for Inviscid Compressible Flows on Unstructured Meshes'', Int. Jl. Num. Meth. Fluids, Vol. 28, pp. 1481-1501.

Thank you for your response. I have to clarify the nature of the problem I try to solve.

The throughflow is used in the field of turbomachinery and consider the flow as axisymetric. The five equations of Euler are solved on a bidimensionnal grid. The effect of the blade row on the flow is introduced by mean of a force (source term) in the momentum and energy equations (so no wall bc has to be imposed to simulate the presence of the blade). The problem is that the sudden application of this force on the first cell following the leading edge lead to entropy generation.

I would like to know if this problem is inherent to the formulation of the FV throughflow or if a specific numerical technique can help me (I use the Roe scheme).

I have a colleague who did his PhD on just this kind of problems. This was at Chalmers University - see http://www.tfd.chalmers.se His name is Stephane Baralon. If you want I can probably arrange a copy of his PhD thesis for you (assuming that you haven't got it already). I have a vague memory that he worked on the leading edge problems and developed some special techniques to handle that.

If you email me I can also give you his email address.

I came across this paper which is related. It looks at spurious entropy production in Euler computations and proposes a hybrid scheme where an entropy conservation equation is solved in isentropic regions thus explicitly enforcing constancy of entropy. Near shocks it switches to momentum equations. The paper is

"Elimination of Spurious Loss in Euler Equation Computations"

Mark Drela, Ali Merchant, Jaime Peraire

You can download it from

http://raphael.mit.edu/pubs.html

Praveen,

Thank you to respond me again. I hope this paper will help me to deal witm my source terms.

Regards,

Jean-François