Speaker: Xuan Gu, Graduate Student, Department of Mathematical Sciences
Date: Wednesday, October 27, 2021, 3:25 PM – 3:40 PM
Title: Uncertainty Quantification for Rayleigh-Taylor Instability
Abstract: The influence of initial conditions on the evolution of the hydrodynamic instabilities has been investigated through laboratory experiments. and simulations over several decades. In this talk, we present the computational framework developed to investigate the effect of initial conditions on the growth rate of Rayleigh-Taylor Instability (RTI) which occurs when the light fluid is accelerated into the heavier fluid. The framework is used to determine the sensitivity of the growth rate with respect to the input parameters on the numerical simulations of flows using a front tracking method. Ensemble data consist of paired sets of input parameters and simulation output results. In the preparation of paired input parameters, the min-max range is specified for values such as Atwood number, gravity and pressure at the interface. Front tracking based computational fluid dynamics (CFD) code is ran for the paired input parameters in order to collect output for the post-processing stage to perform the global sensitivity analysis. The framework couples the Uncertainty Quantification Toolkit (UQTk) C++/python open source library and the CFD code for the sensitivity analysis. We present numerical results to show a large ensemble data to present the influence of initial conditions on the growth rate of RTI.
Speaker: James Burton, Graduate Student, Department of Mathematical Sciences
Date: Wednesday, October 27, 2021, 3:45 PM – 4:00 PM
Title: A Random Choice Method of the Glimm’s Scheme
Abstract: Numerical methods for the solution of hyperbolic partial differential equations concerns shock formation and propagation. In order to solve the Euler equations of compressible fluid dynamics, one needs to use stable, accurate and robust algorithms for shock computations. In our numerical simulations of compressible multiphase flows in 1D, we use Glimm’s scheme because of its good algorithmic properties. However, this scheme is difficult to extend to multidimensional hyperbolic problems. Glimm’s scheme, designed using the random choice method (RCM), is revisited to investigate convergence properties using low-discrepancy sampling methods. A set of van der Corput sampling sequences and its generalized version Halton sequences are used to determine the sensitivity of the random variables to the approximated solutions. A detailed study is performed to find the optimal choice in sampling sequence. Numerical solutions on the various meshes using different sequences are performed to determine the optimal sampling choice with a good convergence property.
Speaker: Ryan Holley, Graduate Student, Department of Mathematical Sciences
Date: Wednesday, October 27, 2021, 4:05 PM – 4:20 PM
Title: High-order WENO Schemes for Richtmyer-Meshkov Instability of
an air/SF_6 interface
Abstract: Turbulent mixing due to Richtmyer-Meshkov Instability (RMI) occurs in a wide range of science and engineering applications such as supernova explosions and inertial confinement fusion. The experimental, theoretical and numerical studies help us to understand the RMI mechanism on these important problems. In this talk, we will present the algorithmic features used for the numerical simulations of RMI and the numerical effects of the high-order Weighted Essentially Non-Oscillatory (WENO) schemes on the two-dimensional RMI of an air/SF$_6$ interface. The single-mode shock-tube experiments of Collins and Jacobs (2002) are used to setup the initial conditions of our numerical simulations. The numerical simulations are performed using high-order WENO scheme to evaluate the asymptotic growth rate of the mixing zone. For validation and verification purpose, we compare our numerical results with experiment and investigate the convergence properties of flow fields under mesh refinement through three-level resolutions (coarse-medium-fine) before and after re-shock. We also study the effect of artificial compression method to the WENO scheme on the computation of shocks and contact discontinues.
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