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Below a new method of solving the solid-fluid coupling within compressible flows with shocks is presented. The method is based on the immersed body method in which the interaction between the solid and fluid is resolved by the introduction of a numerical delta function around the solid.
This delta function is numerically realised by introducing a thin shell of three dimensional elements around the solid and exchanging forcing between the solid and fluid conservatively using newly developed mesh to mesh conservative interpolation methods.
The applications demonstrate the approach for compressible flows with shocks interacting with solids. The solid model is based on the finite element method discrete element method FEMDEM and the fluids model based on a new mixed finite element control volume method which conserves mass in the presence of the solid.
In all problems presented here there is a high density/pressure region on the left and the domain is closed other than on the right.

Phase volume fraction and adaptive meshes. Domain intially filled by oil and irreducible water. Water is injected over the left. Water and oil extracted over the right
New reservoir simulator