deforming mesh and freestream preservation
Hello,
I am currently trying to code an 2D Eulereq solver using the BeamWarming scheme for a given deforming mesh. So far, I can't preserve freestream using my solver (embarrassing ...) for deforming grids. The freestream is conserved for a nondeforming grid. My current understanding is that the mesh deformation (mesh velocity) is accounted for in the solution through the Jacobian which transforms the grid from the cartesian coordinate to generalized bodyfitted coordinate. I also satisfy the Geometric Conservation Law by calculating the grid metrics written the conservative form, suggested by Thomas and Lombard. Should I be including the grid velocity in the flux terms? I have went to many literatures that use BeamWarming scheme and none of them mention this. Any help, suggestion, or comment will be very much appreciated. thank you. Paul 
You need to include the grid velocity terms in the fluxes, since the flux across the face depends on the fluid velocity relative to the face. Additionally, Thomas and Lombard describe a procedure for ensuring geometric conservation when the grid is moving that involves the proper construction of the time derivative of the Jacobian.

thank you. I'll try it.
paul 
I would like some clarification.
I have seen many papers using ALE formulation which includes the grid velocities in the fluxes to accommodate for nonrigidly deforming grids. But I also see papers (ex. Visbal, "On the Use of HigherORder FiniteDifference Schemes on Curviilinear and Deforming Meshes") that does not mention including the grid velocities in the flux. In Visbal paper, he uses the same timeimplicit method that I use which the BeamWarming scheme. so is including the grid velocity necessary? or does Visbal imply that grid velocities are already included in the velocity terms? thank you. Paul 
Sorry  I should have been clearer in my original post. The grid velocities are included in the flux terms, but they appear in the form of the grid time metrics (the time derivatives of the grid transformation terms). The Jacobian relationship in ThomasLombard connects the time derivative of the Jacobian to the spatial variation of the time metric terms. All of this is necessary for GCL.

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