Thesis (M.Sc.) - Cairo University - Faculty Of Engineering - Department Of Electrical Power and Machines

The least - squares finite element method is used to solve the compressible Euler equations in both 2 - D Cartesian and axisymmetric formsSince the method is naturally diffusive , no explicit artificial viscosity is added to the for - mulationThe inherent artificial viscosity , however , is usually large and hence does not allow sharp resolution of discontinuities unless extremely fine grids are usedTo remedy this problem , while retaining the advantages of the least squares method , a moving - node grid adaptation technique is usedThe out - standing feature of the adaptive method is its sensitivity to directional features like shock waves , leading to the automatic construction of adapted grids where the element edge (s) are strongly aligned with such flow phenomena

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