MME Seminar Series: The Dynamics and Thermodynamics of Gas Dynamic Shock Waves

This seminar presents a computational investigation of shock-wave structures through a novel
implicit high-order Galerkin finite element Runge–Kutta algorithm. The algorithm induces no spatial
discretization artificial diffusion, relies on cubic and higher-degree elements for an accurate resolution
of the steep shock gradients, uses an implicit time integration for swift convergence to steady states,
and employs original Neumann-type outlet boundary conditions in the form of generalized Rankine
Hugoniot conditions on normal stress and balance of heat flux and deviatoric-stress work per unit time.
Through an innovative approach, the formulation also calculates the shock extent, which is an additional
unknown, and employs the single non dimensional (0, 1) computational domain for the determination
of any shock structure. The algorithm rapidly generates steady shock structures, in at most 150 time
steps for any upstream Mach number considered in this study, in the range 1.05 < M < 10.0. The finite
element discretization is shown to be asymptotically convergent under progressive grid refinements, in
respect of both the H0 and H1 error norms, with an H0 accuracy order as high as 6 and reduction of the
discretization error to the round-off-error threshold of 1 x10-9 with just 420 computational cells and
5th-degree elements. For any upstream Mach number, the computational results are shown to satisfy the
Rankine–Hugoniot conditions, an established requirement for solution reliability.

MME Seminar_Flyer_Iannelli_03.01.2019