One-Dimensional, One-Phase and Two-Phase Eulerian Explicit Shock Tube Simulation Code

TL;DR

This paper presents a MATLAB-based one-dimensional Eulerian simulation code for single-phase and two-phase systems, validated with the Sod shock tube problem, and incorporates a multi-fidelity surrogate model for uncertainty analysis in multiphase shock interactions.

Contribution

Developed a novel Eulerian simulation code for both single and two-phase flows, including uncertainty propagation with a multi-fidelity surrogate model.

Findings

Code accurately models shock tube problems with exact solution verification.

Uncertainty in particle curtain density was effectively propagated using the surrogate model.

Multi-fidelity approach reduces computational cost for uncertainty analysis.

Abstract

In this work, a one-dimensional simulation code was developed for both single-phase and two-phase systems, focusing on time-dependent Euler equations for gas and particles. These equations, non-linear hyperbolic conservation laws, describe the dynamics of compressible materials, where body forces, viscous stresses, and heat flux are neglected. The Euler equations were discretized using the finite volume method, and the code was written in MATLAB. To test the accuracy of the computational fluid code, the Sod shock tube problem, a physical analogue of the Riemann problem, was employed. This problem models a pressure discontinuity where high and low-pressure regions are separated by a diaphragm, which breaks at t=0, creating a discontinuity in density as well. Exact solutions were used for code verification. A key focus was on modeling a curtain of particles impacted by a shock wave, relevant to multiphase heterogeneous cylindrical explosion studies by the PSAAP II project. This initiative, funded by the US Department of Energy (DOE) National Nuclear Security Administration (NNSA) Office of Advanced Simulation and Computing (ASC), involves Sandia National Laboratories and the Center for Compressible Multiphase Turbulence at the University of Florida. The propagation of uncertainties in the maximum density of the particle curtain was studied by varying initial curtain thickness and initial high density. Given the computational expense of multiple code evaluations for uncertainty propagation, a multi-fidelity surrogate model combining low and high-fidelity simulations was implemented. This model facilitated uncertainty propagation using DAKOTA, a flexible and extensible interface between analysis codes and iterative systems analysis methods.