Many real-world problems involve fluids in motion. The goal of this book is to propose a new
approach to numerical analysis of the underlying nonlinear equations in the spirit of the …

Abstract We consider the Navier–Stokes–Fourier system governing the motion of a general
compressible, heat conducting, Newtonian fluid driven by random initial/boundary data …

We show a general stability result in the framework of strong solutions of the Navier–Stokes–
Fourier system describing the motion of a compressible viscous and heat conducting gas. As …

The instance of the epistemic uncertainty quantification concerning the estimation of the
approximation error norm is analyzed using the ensemble of numerical solutions obtained …

We propose and study the framework of dissipative statistical solutions for the
incompressible Euler equations. Statistical solutions are time-parameterized probability …

We present and discuss a novel approach to deal with conservation properties for the
simulation of nonlinear complex porous media flows in the presence of the following:(1) …

The goal of this paper is to study convergence and error estimates of the Monte Carlo
method for the Navier–Stokes equations with random data. To discretize in space and time …

We develop a method to compute effectively the Young measures associated to sequences
of numerical solutions of the compressible Euler system. Our approach is based on the …

This work presents the development, performance analysis and subsequent optimization of
a GPU-based spectral hyperviscosity solver for turbulent flows described by the three …

We prove the conservation of energy for weak and statistical solutions of the two-
dimensional Euler equations, generated as strong (in an appropriate topology) limits of the …