Variational Formulation of 1—D Unsteady Compressible Flow in a Deforming Tube

The variational principles for 1-D unsteady compressible flow in a deforming tube derived in a previous paper^[1] are improved essentially by reconstructing the initial/final-integral terms according to a new method suggested in a recent paper[2],As a result,the inherent shortcoming of variational principles of being unable to admit physically rational initial/final-value conditions in initial/boundary-value problems is successfully eliminated.Thus,a new theoretical basis for the time-space finite-element analysis is provided.