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### The left hand sides of the equation systems

Subsequently the left hand side for the energy system, the momentum system, the pressure system and the turbulence system are calculated in subroutines mafilltlhs.f, mafillvlhs.f, mafillplhs.f and mafillklhs.f, respectively. For compressible fluids all systems are lumped in subroutine lump.f. The lumped matrix is diagonal. However, the lumped matrix is not stored as such. Indeed, out of efficiency considerations the diagonal of the original matrix, stored in field adb, is replaced by itself minus the lumping matrix. The inverse of the lumping matrix is stored in adl. For incompressible fluids all equation systems except for the pressure equations are lumped. For the pressure equations a LU decomposition is performed for later use in the solution phase of all systems of equations.

At this point the preparation phase is finished an the major loop starts calculating the solution at the subsequent time points