A standard paradigm for the existence of solutions in fluid dynamics is based on the
construction of sequences of approximate solutions or approximate minimizers. This …

We review uncertainty quantification (UQ) for hyperbolic systems of conservation (balance)
laws. The input uncertainty could be in the initial data, fluxes, coefficients, source terms or …

In this work we apply the Continuation Multi-Level Monte Carlo (C-MLMC) algorithm
proposed in Collier et al.(2014) to efficiently propagate operating and geometric …

In this work, we present a model order reduction (MOR) technique for hyperbolic
conservation laws with applications in uncertainty quantification (UQ). The problem consists …

This paper is concerned with generalized polynomial chaos (gPC) approximation for first-
order quasilinear hyperbolic systems with uncertainty. The one-dimensional (1D) hyperbolic …

We develop a class of stochastic numerical schemes for Hamilton--Jacobi equations with
random inputs in initial data and/or the Hamiltonians. Since the gradient of the Hamilton …

This works deals with sensitivity analysis (SA) for the Navier‐Stokes equations. The aim is to
provide an estimate of the variance of the velocity field when some of the parameters are …

In this paper we extensively study the stochastic Galerkin scheme for uncertain systems of
conservation laws, which appears to produce oscillations already for a simple example of …

We introduce an operator splitting based stochastic Galerkin method for the one-
dimensional compressible Euler equations with random inputs. The method uses a …

Continuous sedimentation processes in a clarifier-thickener unit can be described by a
scalar nonlinear conservation law whose flux density function is discontinuous with respect …