Statistical error analysis in numerical solutions of shock physics problems

We seek robust and understandable error models for shock physics simulations. The purpose of our study is to formulate and validate a composition law to estimate errors in the solutions of composite problems in terms of the errors from simpler ones.; The problem study in one spatial dimension has been generated by a shock wave interacting with a contact, located near a reflecting wall for planar geometry. The transmitted shock reflects between the contact and the wall or origin. For each interaction, we performed numerical simulations on an ensemble of 200 initial conditions perturbed from a base case to find input/output relations for the errors in such interactions. We develop a, wave filter, which is the fundamental diagnostic tool that identifies individual waves and measures the position and the width of numerical waves. We see that a very simple model of solution error is sufficient for the study of a highly nonlinear problem. The error is linear in the input wave strengths. A composition law for combining errors and predicting errors for composite interactions on the basis of an error model of the simple constituent interactions is formulated and validated.; We are also interested in the analysis of error in is the 2D instability in the Richtmyer-Meshkov (RM) setup. Because of complexity of the chaotic flow in RM, we need reduced descriptions of the flow. In many purposes, a detailed pointwise description of the chaotic flow is not needed. The flow is highly unstable and not reproducible. Rather, statistical averages of the flow are important. These will be stable and reproducible in the sense of pointwise quantities. The goal is to establish probabilistic error models for statistical observables in numerical simulations of chaotic flow. Our main result for the 2 D case are the development of tools need for data analysis of the chaotic simulations. We developed radial averaging algorithms and a two dimensional wave filter to analyze the chaotic flow simulation.