Related papers: Improving convergence of volume penalised fluid-so…

We study the finite element approximation of the solid isotropic material with penalization method (SIMP) for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local…

We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…

We present a novel immersed boundary method that implements acoustic perturbation theory to model an acoustically levitated droplet. Instead of resolving sound waves numerically, our hybrid method solves acoustic scattering…

A systematic study is carried out on a fully resolved fluid-particle model which couples the Lattice Boltzmann Method (LBM) and the Discrete Element Method (DEM) using an immersed moving boundary technique. Similar algorithms have been…

In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…

We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…

We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical…

The multi-direct-forcing immersed boundary method allows for a small velocity error of the no-slip condition in moving-particle problems but suffers from numerical instability if simulation parameters are not carefully chosen. This study…

This article presents a priori error estimates of the miscible displacement of one incompressible fluid by another through a porous medium characterized by a coupled system of nonlinear elliptic and parabolic equations. The study utilizes…

This paper proposes an approach combining the Volume Penalization (VP) and the the Lattice Boltzmann method (LBM) to compute fluid structure interaction involving rigid bodies. The method consists in adding a force term in the LBM…

A novel simulation framework has been developed in this study for the direct numerical simulation of the aerodynamic breakup of a vaporizing drop. The interfacial multiphase flow with phase change is resolved using a consistent geometric…

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a…

In this work, we consider a constrained convex problem with linear inequalities and provide an inexact penalty re-formulation of the problem. The novelty is in the choice of the penalty functions, which are smooth and can induce a non-zero…

We design an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two…

Given a hypothesis space, the large volume principle by Vladimir Vapnik prioritizes equivalence classes according to their volume in the hypothesis space. The volume approximation has hitherto been successfully applied to binary learning…

To study the dynamics of particles in turbulence when their sizes are comparable to the smallest eddies in the flow, the Kolmogorov length scale, efficient and accurate numerical models for the particle-fluid interaction are still missing.…

We develop a numerical method for solving a free boundary problem which describes shape relaxation, by surface tension, of a long and thin bubble of an inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell. The method of…

Incompressibility is a fundamental condition in most fluid models. Accumulation of simulation errors violates it and causes volume loss. Past work suggested correction methods to battle it. These methods, however, are imperfect and in some…