Related papers: Adaptive Time Stepping for Vesicle Suspensions
The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…
We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier-slip condition such that the velocity equation can be posed in mixed form with the vorticity as an…
Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in {[Qiu and…
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…
A dual time-stepping strategy of gas-kinetic scheme for the simulation of unsteady flows is introduced in this work. The dual time-stepping strategy is always used in the approaches of unsteady flows, and the ability of dual time-stepping…
We generalize the explicit high-order positivity-preserving entropy stable spectral collocation schemes developed in Upperman 2023 and Yamaleev 2023 for the three-dimensional (3D) compressible Navier Stokes equations to a time implicit…
We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck…
Vesicle suspensions appear in many biological and industrial applications. These suspensions are characterized by rich and complex dynamics of vesicles due to their interaction with the bulk fluid, and their large deformations and nonlinear…
We study a recent timestep adaptation technique for hyperbolic conservation laws. The key tool is a space-time splitting of adjoint error representations for target functionals due to S\"uli and Hartmann. It provides an efficient choice of…
This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…
We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…
In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schr\"odinger equation with multiplicative noise. Based on the splitting…
For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and numerical convergence can be demonstrated using a resolution…
Spectral deferred corrections (SDC) are a class of iterative methods for the numerical solution of ordinary differential equations. SDC can be interpreted as a Picard iteration to solve a fully implicit collocation problem, preconditioned…
For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…
Semi-implicit spectral deferred correction (SDC) methods provide a systematic approach to construct time integration methods of arbitrarily high order for nonlinear evolution equations including conservation laws. They converge towards $A$-…
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or different initial condition data, boundary conditions data,…
The aim of this paper is to propose a high performance control approach for trajectory tracking of Autonomous Underwater Vehicles (AUVs). However, the controller performance can be affected by the unknown perturbations including model…