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A low diffusive flux difference splitting based kinetic scheme is developed based on a discrete velocity Boltzmann equation, with a novel three velocity model. While two discrete velocities are used for upwinding, the third discrete…
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…
The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the…
We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…
We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved…
Stochastic Model Predictive Control has proved to be an efficient method to plan trajectories in uncertain environments, e.g., for autonomous vehicles. Chance constraints ensure that the probability of collision is bounded by a predefined…
Stochastic variance reduced optimization methods are known to be globally convergent while they suffer from slow local convergence, especially when moderate or high accuracy is needed. To alleviate this problem, we propose an optimization…
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…
A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…
Predicting particle segregation has remained challenging due to the lack of a general model for the segregation velocity that is applicable across a range of granular flow geometries. Here, a segregation velocity model for dense granular…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
We introduce a general-purpose method for optimising the mixing rate of advective fluid flows. An existing velocity field is perturbed in a $C^1$ neighborhood to maximize the mixing rate for flows generated by velocity fields in this…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
Small-scale features of shallow water flow obtained from direct numerical simulation (DNS) with two different computational codes for the shallow water equations are gathered offline and subsequently employed with the aim of constructing a…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
We present a numerical comparison between two standard finite volume schemes and a discontinuous Galerkin method applied to the BGK equation of rarefied gas dynamics. We pay a particular attention to the numerical boundary conditions in…
Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to…
We consider two-grid mixed-finite element schemes for the spatial discretization of the incompressible Navier-Stokes equations. A standard mixed-finite element method is applied over the coarse grid to approximate the nonlinear…