Related papers: Spatial coupling of an explicit temporal adaptive …
The periodic hills simulation case is a well-established benchmark for computational fluid dynamics solvers due to its complex features derived from the separation of a turbulent flow from a curved surface. We study the case with the…
Following on our previous work [S. Delong and B. E. Griffith and E. Vanden-Eijnden and A. Donev, Phys. Rev. E, 87(3):033302, 2013], we develop temporal integrators for solving Langevin stochastic differential equations that arise in…
Non-hydrostatic atmospheric models often use semi-implicit temporal discretisations in order to negate the time step limitation of explicitly resolving the fast acoustic and gravity waves. Solving the resulting system to machine precision…
This paper presents a Crank-Nicolson leap-frog (CNLF) scheme for the unsteady incompressible magnetohydrodynamics (MHD) equations. The spatial discretization adopts the Galerkin finite element method (FEM), and the temporal discretization…
In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our…
We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to the Reynolds number. While both methods rely on a HHO formulation of the viscous term, the…
Recently, our group developed explicit symplectic methods for curved spacetimes that are not split into several explicitly integrable parts, but are via appropriate time transformations. Such time-transformed explicit symplectic integrators…
The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…
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…
In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. We follow a method of lines approach and utilize an underlying…
We consider time dependent thermal fluid structure interaction. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet-Neumann method and a fixed…
To plan the trajectories of a large-scale heterogeneous swarm, sequentially or synchronously distributed methods usually become intractable due to the lack of global clock synchronization. To this end, we provide a novel asynchronous…
Two phase flows that include phase transition, especially phase creation, with a sharp interface remain a challenging task for numerics. We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase.…
In this work, we design and analyze semi/fully-discrete virtual element approximations for the time-dependent Navier--Stokes-Cahn--Hilliard equations, modeling the dynamics of two-phase incompressible fluid flows with diffuse interfaces. A…
We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…
We describe an implicit general relativistic hydrodynamics code. The evolution equations are formulated in comoving coordinates. A conservative finite differencing of the Einstein equations is outlined, and artificial viscosity and…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…
Time-implicit schemes are attractive since they allow numerical time steps that are much larger than those permitted by the Courant-Friedrich-Lewy criterion characterizing time-explicit methods. This advantage comes, however, with a cost:…
Adaptive second-order Crank-Nicolson time-stepping methods using the recent scalar auxiliary variable (SAV) approach are developed for the time-fractional Molecular Beam Epitaxial models with Caputo's derivative. Based on the piecewise…