We present a parallel explicit/implicit time integration scheme well suited for blockadaptive grids. The basic idea of the algorithm is that the time stepping scheme can differ in the blocks of the grid for a given time step: an explicit scheme is used in the blocks where the local stability requirement is not violated and an implicit scheme is used in the blocks where the explicit scheme would...

The purpose of this study is to enhance the stability properties of our recentlydeveloped numerical method [D. Kamensky, M.-C. Hsu, D. Schillinger, J.A. Evans, A. Aggarwal, Y. Bazilevs, M.S. Sacks, T.J.R. Hughes, “An immersogeometric variational framework for fluid–structure interaction: Application to bioprosthetic heart valves”, Comput. Methods Appl. Mech. Engrg., 284 (2015) 1005–1053] for im...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit time stepping used the temporal discretization, which allows much larger step size stability compared to explicit methods, especially low-Mach number flows and/or on highl...

We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping scheme for differential linear complementarity systems (DLCS). We choose a specific solution from the solution set of the linear complementarity constraints to define a locally Lipschitz continuous right-hand-side function in...

In this paper we present an implicit time-stepping scheme for multibody systems with intermittent contact by incorporating the contact constraints as a set of complementarity and algebraic equations within the dynamics model. Two primary sources of stability and accuracy problems in prior time stepping schemes for differential complementarity models of multibody systems are the use of polyhedra...

In this paper a new time-stepping method for simulating systems of rigid bodies is given. Unlike methods which take an instantaneous point of view, our method is based on impulse-momentum equations, and so does not need to explicitly resolve impulsive forces. On the other hand, our method is distinct from previous impulsive methods in that it does not require explicit collision checking and it ...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

In this work, we will analyze a class of large time-stepping methods for the Cahn–Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerica...

In [13], we had performed numerical comparisons for different time stepping schemes for the incompressible Navier-Stokes equations. In this paper, we present the numerical analysis in the context of the Navier-Stokes equations for a new time-stepping θ-scheme which has been recently proposed by Glowinski [5]. Like the well-known classical FractionalStep-θ-scheme which had been introduced by Glo...