1-D COMPRESSIBLE FLOW IN EULERIAN FRAME OF REFERENCE WITH IDEAL GAS BEHAVIOR USING p-VERSION STLSFEF

摘要

This paper presents a p-version 'space-time least squares finite element formulation' (STLSFEF) for one dimensional time dependent compressible flow in an Eulerian frame of reference with ideal gas law in which all dependent variables exhibit Simultaneous dependence on space and time. Flow is considered laminar, inviscid and non-heat-conducting. Using the dimensionless form of continuity, momentum and energy equations in density (ρ), pressure (p) and velocity (u), ρ, p and u are interpolated in space and time using equal order C{sup}0 interpolations. The element, properties are derived by minimizing the space-time integral of the sum of squares of the errors or residuals (called error functional) resulting from the three differential equations. A time marching procedure is utilized to advance the solution in time in which the solution for the current time step provides the initial conditions for the next time step. Proposed formulation is free of inherent' and numerical diffusion and provides ability to control errors in each time step. The proposed approach is free of stability problems which always plague space-time decoupled methods. A numerical example of closed end shock tube which combines simultaneous compression and rarefaction is presented at low Mach numbers. Applicability and effectiveness of the proposed formulation is demonstrated for low Mach number compressible flops and a discussion is presented for its extension to high Mach number flows.