Related papers: A provably efficient monotonic-decreasing algorith…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
We consider the interaction between a poroelastic structure, described using the Biot model in primal form, and a free-flowing fluid, modelled with the time-dependent incompressible Stokes equations. We propose a diffuse interface model in…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
Although the Smoothed Particle Hydrodynamics (SPH) method has been demonstrated as a promising numerical solver for multiphase flow problems due to its Lagrangian nature, its application to complex channel flow may encounter additional…
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…
Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…
A scale-resolving simulation methodology that includes stochastic energy backscatter is incorporated into a proprietary block-structured compressible flow solver. Particular attention is devoted to the discretisation of the convective terms…
We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time for the error between the solution of the numerical scheme,…
The log-homotopy particle flow filter resolves the Bayesian update by transporting particles along a continuous trajectory in pseudo-time. However, the governing partial differential equation for the flow velocity is fundamentally…
An efficient topology optimization method applicable to both continuum and rarefied gas flows is proposed in the framework of gas-kinetic theory. The areas of gas and solid are marked by the material density, based on which a fictitious…
A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
The manipulation of a collection of fluid particles in a low Reynolds number environment has several important applications. As we demonstrate in this paper, this manipulation problem is related to the scientific question of how fluid flow…
Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order…
This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the…
In this report, we propose a new adaptive time filter algorithm for the unsteady Stokes/Darcy model. First we present a first order ${\theta}$-scheme with the variable time step which is one parameter family of Linear Multi-step methods and…
This work presents a new multiphase SPH model that includes the shifting algorithm and a variable smoothing length formalism to simulate multi-phase flows with accuracy and proper interphase management. The implementation was performed in…
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…
The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…