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Abstract
A modified finite element method is used to solve the equations of motion for inviscid and viscous two-dimensional compressible flow. The time-dependent equations are solved explicitly using bilinear isoparametric quadrilateral elements, mass lumping, and Petrov-Galerkin weighting applied to the advection terms. Use of reduced integration is optional, along with h adaptation (with 2×2 quadrature). The modified FEM is accurate, providing the elements are not too distorted (using reduced integration). Problems requiring several thousand nodes can be run on a personal computer.