A second-order, time integration scheme for calculating stratified incompressible flows

1976 ◽  
Vol 22 (1) ◽  
pp. 74-86 ◽  
Author(s):  
Robert K.-C Chan
Keyword(s):  
Incompressible Flows ◽  
Time Integration ◽  
Second Order ◽  
Integration Scheme ◽  
Time Integration Scheme

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

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
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.

UNSTEADY FLOW COMPUTATIONS OVER MOVING BODY USING DYNAMIC MESHES

2004 ◽  
Vol 01 (03) ◽  
pp. 507-518
Author(s):  
J. C. MANDAL ◽  
J. BALLMANN
Keyword(s):  
Compressible Flows ◽  
Time Integration ◽  
Time Discretization ◽  
Second Order ◽  
Integration Scheme ◽  
Arbitrary Lagrangian Eulerian ◽  
Time Step ◽  
Naca0012 Airfoil ◽  
Moving Body ◽  
Time Integration Scheme

An efficient implicit unstructured grid algorithm for solving unsteady inviscid compressible flows over moving body employing an Arbitrary Lagrangian Eulerian formulation is presented. In the present formulation, the time discretization is performed using a second-order accurate 3-point time integration scheme and the upwind-biased space discretization using second-order accurate finite volume formulation with Venkatakrishnan limiter. The face-velocities of the control volumes are computed using Geometric Conservation Laws. The nonlinear system arising from the implicit formulation is solved using an ILU preconditioned Newton–Krylov iteration at every time step. The computed results for two test cases involving harmonically oscillating NACA0012 airfoil are presented in order to demonstrate the efficacy of the present solver.

Design for a Hybrid Absorbing Element in the Time Domain Using PML and Infinite Element Concepts

2014 ◽  
Author(s):  
Jeffrey L. Cipolla
Keyword(s):  
Time Domain ◽  
Time Integration ◽  
Low Frequency ◽  
Second Order ◽  
Integration Scheme ◽  
Lumped Mass ◽  
Central Difference ◽  
Infinite Element ◽  
Time Integration Scheme ◽  
The Time Domain

We introduce an approach blending the Perfectly Matched Layer (PML) and infinite element paradigms, to achieve better performance and wider applicability than either approach alone. In this paper, we address the specific challenges of unbounded problems when using time-domain explicit finite elements: 1. The algorithm must be spatially local, to minimize storage and communication cost, 2. It must contain second-order time derivatives for compatibility with the explicit central-difference time integration scheme, 3. Its coefficient for the second-order derivatives must be diagonal (“lumped mass”), 4. It must be time-stable when used with central-differences, 5. It must converge to the correct low-frequency (Laplacian) limit, 6. It should exhibit high accuracy across typically encountered dynamic frequencies, i.e. at short to long wavelengths, 7. Its user interface should be as simple as possible. Here, we will describe the derivation of a time-domain implementation of the hybrid PML/infinite element, and discuss its advantages for implementation.

scholarly journals Structural Reliability Sensitivities under Nonstationary Random Vibrations

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Rita Greco ◽  
Francesco Trentadue
Keyword(s):  
Structural Reliability ◽  
Structural Parameters ◽  
Time Integration ◽  
Structural Response ◽  
Integration Scheme ◽  
Structural Systems ◽  
Frame Building ◽  
Time Integration Scheme ◽  
Noise Input ◽  
The Time Domain

Response sensitivity evaluation is an important element in reliability evaluation and design optimization of structural systems. It has been widely studied under static and dynamic forcing conditions with deterministic input data. In this paper, structural response and reliability sensitivities are determined by means of the time domain covariance analysis in both classically and nonclassically damped linear structural systems. A time integration scheme is proposed for covariance sensitivity. A modulated, filtered, white noise input process is adopted to model the stochastic nonstationary loads. The method allows for the evaluation of sensitivity statistics of different quantities of dynamic response with respect to structural parameters. Finally, numerical examples are presented regarding a multistorey shear frame building.

scholarly journals A new energy–momentum time integration scheme for non-linear thermo-mechanics

2020 ◽  
Vol 372 ◽  
pp. 113395 ◽  
Author(s):  
R. Ortigosa ◽  
A.J. Gil ◽  
J. Martínez-Frutos ◽  
M. Franke ◽  
J. Bonet
Keyword(s):  
Time Integration ◽  
Integration Scheme ◽  
Non Linear ◽  
New Energy ◽  
Time Integration Scheme

New insights into the β1/β2-Bathe time integration scheme when L-stable

2021 ◽  
Vol 245 ◽  
pp. 106433
Author(s):  
Mohammad Mahdi Malakiyeh ◽  
Saeed Shojaee ◽  
Saleh Hamzehei-Javaran ◽  
Klaus-Jürgen Bathe
Keyword(s):  
Time Integration ◽  
Integration Scheme ◽  
Time Integration Scheme

scholarly journals Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations

2018 ◽  
Author(s):  
Tuomas Kärnä ◽  
Stephan C. Kramer ◽  
Lawrence Mitchell ◽  
David A. Ham ◽  
Matthew D. Piggott ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Unstructured Grid ◽  
Splitting Method ◽  
Time Integration ◽  
River Estuary ◽  
Coastal Ocean ◽  
Second Order ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Element Discretization

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.

Energy‐momentum consistent time integration scheme for non‐linear electro‐elastodynamics

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Alexander Janz ◽  
Peter Betsch ◽  
Marlon Franke ◽  
Rogelio Ortigosa
Keyword(s):  
Time Integration ◽  
Integration Scheme ◽  
Non Linear ◽  
Time Integration Scheme
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