VERIFYING & VALIDATING THE INTEGRO-DIFFERENTIAL SCHEME CAPABILITY TO SOLVE THE 1D UNSTEADY GAS DYNAMIC EQUATIONS

Recently, an unsteady Integro-Differential scheme (IDS) was formulated for use with the unsteady Navier-Stokes equations to simulate complex fluid fields under conditions that include a wide range of Reynolds and Mach numbers. A list of complex CFD problems were solved their flow field. CFD problems that were successfully solved include: jet flows, flow separation for varying Re, shock-vortex interactions, shock boundary-layer interactions, Isolator shock-train simulation and control and two-phase shock-bubble interactions. The IDS results showed that, when provided with the appropriate initial and boundary conditions, the IDS technique simulated the physics within the prescribed flow fields. However, the dissipative, dispersive and error qualities of the newly developed IDS method have not been fully explored. In this effort, the IDS scheme is use to solve six Reimann problems, which are known to present great challenges to existing numerical methods. The results of the IDS scheme are compared to those of the AUSM and WENO schemes. In this effort a comparative analysis of the primitive variables and their associated errors are evaluated and compared over the entire range of the fluid flow and over long periods of simulation time. The predicted results and their errors are compared to the exact solutions, especially in the neighborhood on the shocks, the contact surfaces, the rarefaction waves and within the vacuum. The three schemes, IDS, AUSM and WENO, were implemented in solving nine Reimann problems, under identical conditions. In the end, only solutions from 6 common problems were analyzed, as two of the three schemes were unable to satisfy the numerical experimental conditions. A detailed description of the numerical experiments and their findings are presented herein.