Inertial Coupling Method for particles in an incompressible fluctuating fluid

We develop an inertial coupling method for modeling the dynamics of point-like 'blob' particles immersed in an incompressible fluid, generalizing previous work for compressible fluids. The coupling consistently includes excess (positive or negative) inertia of the particles relative to the displaced fluid, and accounts for thermal fluctuations in the fluid momentum equation. The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation-dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatio-temporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels make the discrete blob a particle with surprisingly physically-consistent volume, mass, and hydrodynamic properties. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation-dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and associated discussion) relative to published versio

Geometric Numerical Integration

The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of numerical methods

Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal approximation. This explicit time integrator allows for mean-square error bounds independent of the space discretisation and thus do not suffer from a step size restriction as in the often used St\"ormer-Verlet-leap-frog scheme. Furthermore, it satisfies an almost trace formula (i.e., a linear drift of the expected value of the energy of the problem). Numerical experiments are presented and confirm the theoretical results

Geometric Numerical Integration (hybrid meeting)

The topics of the workshop included interactions between geometric numerical integration and numerical partial differential equations; geometric aspects of stochastic differential equations; interaction with optimisation and machine learning; new applications of geometric integration in physics; problems of discrete geometry, integrability, and algebraic aspects

Nonlinear Evolution Equations: Analysis and Numerics

The workshop was devoted to the analytical and numerical investigation of nonlinear evolution equations. The main aim was to stimulate a closer interaction between experts in analytical and numerical methods for areas such as wave and Schrödinger equations or the Navier–Stokes equations and fluid dynamics

Seismic risk assessment of frame structures using stochastic beam-column elements

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) "Analysis and Design of Earthquake Resistant Structures