Compressible fluid motion with uncertain data

TL;DR

This paper develops an analytical framework for the numerical analysis of compressible fluid models with uncertain data, comparing weak and strong stochastic approaches including the stochastic collocation method.

Contribution

It introduces a unified framework for analyzing compressible fluid equations with uncertain data, emphasizing the strong stochastic approach and its numerical implementation.

Findings

Framework applicable to weak and strong stochastic methods

Analysis of stochastic collocation with piecewise constant approximation

Guidelines for numerical analysis of uncertain fluid models

Abstract

We propose a suitable analytical framework to perform numerical analysis of problems arising in compressible fluid models with uncertain data. We discuss both weak and strong stochastic approach, where the former is based on the knowledge of the mere distribution (law) of the random data typical for the Monte-Carlo and related methods, while the latter assumes the data to be known as a random variabble on a given probability space aiming at obtaining the associated solution in the same form. As an example of the strong approach, we discuss the stochastic collocation method based on a piecewise constant approximation of the random data.