Keynote

Effect of Mathematical Model Simplification on Solution Verification Exercises: An Update on Filipe's Work

  • Soares Pereira, Filipe (Los Alamos National Laboratory (posthumous))
  • Koskelo, Aaron (Los Alamos National Laboratory)
  • Wilson, Brandon (Los Alamos)

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At the 2024 WCCM, we presented Filipe’s work as it was at the time [1]. He had been running additional simulations which completed after that presentation. We intend to present his additional work in the context of the original presentation. The body of work evaluates the impact of the Euler Equations (EE) on solution verification and validation of transient multi-material mixing flow simulations. EE are an example of a simplified mathematical model widely used in transient multi-material mixing problems featuring shock waves and high-Mach number flow (e.g., stellar astrophysics, shock-driven mixing, and high-speed combustion). It simplifies the Navier-Stokes equations (NSE) by assuming adiabatic and inviscid flow, i.e., neglect heat conduction, viscous, and diffusivity effects. Despite the EE importance, the continuous enhancement of computing power and numerical methods makes assessing the envelope of such mathematical model crucial. For example, neglecting the molecular viscosity makes the effective Reynolds number of simulations solely determined by the numerical viscosity and assumes an “infinite” Reynolds number. However, how high is a Re high enough? What is the impact of an effective Re uniquely determined by the numerical viscosity on solution verification? Toward this end, we simulate four flows with the EE and the Navier-Stokes Equations (NSE): i) 1D Riemann problem, ii) 2D triple point problem, iii) 3D Taylor Green Vortex, and iv) 3D Richtmyer-Meshkov multi- material flow measured at LANL. The computations are performed on several mesh/time resolutions to evaluate their dependence on this parameter and estimate the numerical uncertainty. From a validation point of view, the results show that inviscid and adiabatic assumptions strongly impact the simulations' physics, hampering comparisons between simulations and reference data. This outcome stems from the inability to bind the effective Re and consider heat conduction. Such assumptions can also impact solution verification exercises by significantly increasing the cost of converging the simulations upon grid refinement and artificially increasing the numerical uncertainty and the cost of solution verification exercises. Overall, the results indicate that modeling assumptions strongly impact not only validation exercises but also solution verification.