ANALYTICAL INTEGRATION AND A NUMERICAL-METHOD FOR I-D COMPRESSIBLE FLOW WITH DIFFUSIVE TRANSPORT

A new analytic integral and a numerical method are presented for l-D c ompressible how; the method is suitable for problems in which diffusiv e scales are of the same order as the length scale of the flow. The co nventional, Eulerian formulation of the compressible flow equations is converted to a Lagrangian formulation by coordinate transform. Therea fter, the balance of linear momentum is integrated once analytically. This procedure yields a set of two nonlinear partial differential equa tions for the particle position and total energy fields; these equatio ns are easily solved using finite differences. As a consequence of the analytic integration, the system is characterized by easily controlle d numerical dispersion and dissipation for a very broad range of Reyno lds or Mach numbers. Solutions are presented for the well-known piston problem; comparison with available analytical results is excellent.