This paper extends an algorithm of P1-conservative interpolation on triangular meshes to tetrahedral meshes and thus constructs an approach of solution reconstruction for three-dimensional problems. The conservation property is achieved by local mesh intersection and the mass of a tetrahedron of the current mesh is calculated by the integral on its intersection with the background mesh. For each current tetrahedron, the overlapped background tetrahedrons are detected efficiently. A mesh intersection algorithm is proposed to construct the intersection of a current tetrahedron with the overlapped background tetrahedron and mesh the intersection region by tetrahedrons. A localization algorithm is employed to search the host units in background mesh for each vertex of the current mesh. In order to enforce the maximum principle and avoid the loss of monotonicity, correction of nodal interpolated solution on tetrahedral meshes is given. The performance of the present solution reconstruction method is verified by numerical experiments on several analytic functions and the solution of the flow around a sphere.

A finite volume method for the simulation of compressible aerodynamic flows is described.Stabilisation and shock capturing is achieved by the use of an HLLC consistent numericalflux function, with acoustic wave improvement. The method is implemented on anunstructured hybrid mesh in three dimensions. A solution of higher order accuracy isobtained by reconstruction, using an iteratively corrected least squares process, and by anew limiting procedure. The numerical performance of the complete approach is demonstratedby considering its application to the simulation of steady turbulent transonic flow overan ONERA M6 wing and to a steady inviscid supersonic flow over a modern military aircraftconfiguration.