A Second Order Accurate Adams-Bashforth Type Discrete Event Integration Scheme

Abstract. Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to real life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability preserving time integration method and slope limiters. Compared to previous DG models advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.

Download Full-text

Second order theory of min-linear systems and its application to discrete event systems

[1991] Proceedings of the 30th IEEE Conference on Decision and Control ◽

10.1109/cdc.1991.261654 ◽

2002 ◽

Cited By ~ 8

Author(s):

G. Cohen ◽

S. Gaubert ◽

R. Nikoukhah ◽

J.P. Quadrat

Keyword(s):

Linear Systems ◽

Discrete Event Systems ◽

Discrete Event ◽

Order Theory ◽

Second Order ◽

Event Systems

Download Full-text

A New Unconditionally Stable Time Integration Method for Analysis of Nonlinear Structural Dynamics

Journal of Applied Mechanics ◽

10.1115/1.4007682 ◽

2013 ◽

Vol 80 (2) ◽

Cited By ~ 6

Author(s):

Ali Akbar Gholampour ◽

Mehdi Ghassemieh ◽

Mahdi Karimi-Rad

Keyword(s):

Time Integration ◽

Second Order ◽

Numerical Dispersion ◽

Computational Time ◽

Numerical Dissipation ◽

Integration Scheme ◽

Time Step ◽

Similar Time ◽

Unconditionally Stable ◽

Average Acceleration

A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better accuracy than the classical methods. By considering this assumption and employing two parameters δ and α, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the accuracy of the proposed method. Second order accuracy is achieved for all values of δ and α. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-θ, and generalized-α methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally stable methods, namely, Newmark's average acceleration, Wilson-θ, and generalized-α methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step duration, the proposed method is shown to be faster in comparison with the other methods.

Download Full-text

A Second Order Finite Difference Integration Scheme Using the Compatibility Relations

Boundary Algorithms for Multidimensional Inviscid Hyperbolic Flows ◽

10.1007/978-3-322-85441-4_9 ◽

1978 ◽

pp. 60-67

Author(s):

T. deNeef

Keyword(s):

Finite Difference ◽

Second Order ◽

Integration Scheme

Download Full-text

An iterative integration scheme for solving second-order ordinary differential equations

Advances in Engineering Software ◽

10.1016/0965-9978(93)90012-i ◽

1993 ◽

Vol 16 (3) ◽

pp. 153-159

Author(s):

Stavri Ristani

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Second Order ◽

Integration Scheme ◽

Iterative Integration

Download Full-text

Exponential Time Integration and Second-Order Difference Scheme for a Generalized Black-Scholes Equation

Journal of Applied Mathematics ◽

10.1155/2012/796814 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Zhongdi Cen ◽

Anbo Le ◽

Aimin Xu

Keyword(s):

Difference Scheme ◽

Time Integration ◽

Second Order ◽

Integration Scheme ◽

Uniform Mesh ◽

Central Difference ◽

Exponential Time ◽

Black Scholes ◽

Time Integration Scheme ◽

Exponential Time Integration

We apply an exponential time integration scheme combined with a central difference scheme on a piecewise uniform mesh with respect to the spatial variable to evaluate a generalized Black-Scholes equation. We show that the scheme is second-order convergent for both time and spatial variables. It is proved that the scheme is unconditionally stable. Numerical results support the theoretical results.

Download Full-text