A variational theory for one-dimensional unsteady compressible flow – an image plane approach

Via a semi-inverse method of establishing generalized variational principles, two families of variational principles and generalized variational principles for one-dimensional unsteady compressible flow in an imagine plane τ–Ψ (defined by τ=t,Ψ – path-function) have been deduced. The calculation domain in the image plane has the regular form of rectangle, which gives much advantage of utilizing variational-based FEM or other direct variational methods such as Kantrovich–FEM method to solve the problem.