• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.2
• /
• pp.93-114
• /
• 2019

In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion. We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences. The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first-order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.

• Earthquakes and Structures
• /
• v.14 no.1
• /
• pp.45-53
• /
• 2018

A family of the structure-dependent methods seems very promising for time integration since it can simultaneously have desired numerical properties, such as unconditional stability, second-order accuracy, explicit formulation and numerical dissipation. However, an unusual overshoot, which is essentially different from that found by Goudreau and Taylor in the transient response, has been experienced in the steady-state response of a high frequency mode. The root cause of this unusual overshoot is analytically explored and then a remedy is successfully developed to eliminate it. As a result, an improved formulation of this family method can be achieved.

• Journal of computational fluids engineering
• /
• v.13 no.4
• /
• pp.114-125
• /
• 2008

Current state and perspective of DNS of turbulence and turbulent combustion are discussed with feature trend of the fastest supercomputer in the world. Based on the perspective of DNS of turbulent combustion, possibility of perfect simulations of IC engine is shown. In 2020, the perfect simulation will be realized with 30 billion grid points by 1EXAFlops supercomputer, which requires 4 months CPU time. The CPU time will be reduced to about 4 days if several developments were achieved in the current fundamental researches. To shorten CPU time required for DNS of turbulent combustion, two numerical methods are introduced to full-explicit full-compressible DNS code. One is compact finite difference filter to reduce spatial resolution requirements and numerical oscillations in small scales, and another is well-known point-implicit scheme to avoid quite small time integration of the order of nanosecond for fully explicit DNS. Availability and accuracy of these numerical methods have been confirmed carefully for auto-ignition, planar laminar flame and turbulent premixed flames. To realize DNS of IC engine with realistic kinetic mechanism, several DNS of elemental combustion process in IC engines has been conducted.

• 한국전산유체공학회:학술대회논문집
• /
• 2008.03a
• /
• pp.359-366
• /
• 2008

Current state and perspective of DNS of turbulence and turbulent combustion are discussed with feature trend of the fastest supercomputer in the world. Based on the perspective of DNS of turbulent combustion, possibility of perfect simulations of IC engine is shown. In 2020, the perfect simulation will be realized with 30 billion grid points by 1EXAFlops supercomputer, which requires 4 months CPU time. The CPU time will be reduced to about 4 days if several developments were achieved in the current fundamental researches. To shorten CPU time required for DNS of turbulent combustion, two numerical methods are introduced to full-explicit full-compressible DNS code. One is compact finite difference filter to reduce spatial resolution requirements and numerical oscillations in small scales, and another is well-known point-implicit scheme to avoid quite small time integration of the order of nanosecond for fully explicit DNS. Availability and accuracy of these numerical methods have been confirmed carefully for auto-ignition, planar laminar flame and turbulent premixed flames. To realize DNS of IC engine with realistic kinetic mechanism, several DNS of elemental combustion process in IC engines has been conducted.

• 한국전산유체공학회:학술대회논문집
• /
• 2008.10a
• /
• pp.359-366
• /
• 2008

Current state and perspective of DNS of turbulence and turbulent combustion are discussed with feature trend of the fastest supercomputer in the world. Based on the perspective of DNS of turbulent combustion, possibility of perfect simulations of IC engine is shown. In 2020, the perfect simulation will be realized with 30 billion grid points by 1EXAFlops supercomputer, which requires 4 months CPU time. The CPU time will be reduced to about 4 days if several developments were achieved in the current fundamental researches. To shorten CPU time required for DNS of turbulent combustion, two numerical methods are introduced to full-explicit full-compressible DNS code. One is compact finite difference filter to reduce spatial resolution requirements and numerical oscillations in small scales, and another is well-known point-implicit scheme to avoid quite small time integration of the order of nanosecond for fully explicit DNS. Availability and accuracy of these numerical methods have been confirmed carefully for auto-ignition, planar laminar flame and turbulent premixed flames. To realize DNS of IC engine with realistic kinetic mechanism, several DNS of elemental combustion process in IC engines has been conducted.

• Structural Engineering and Mechanics
• /
• v.65 no.1
• /
• pp.121-128
• /
• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• Transactions of Materials Processing
• /
• v.9 no.3
• /
• pp.313-319
• /
• 2000

Finite element analysis is carried out for simulation of the multi-stage elliptic cup drawing process with the large aspect ratio. The analysis incorporates with shell elements for an elasto-plastic finite element method with the explicit time integration scheme. For the simulation, LS-DYNA3D is utilized for its wide capability of solving forming problems. The simulation result shows that the non-uniform drawing ratio at the elliptic cross section ad the small shoulder radius cause failure such as tearing and wrinkling. The result suggests the guideline to modify the tool shape for prevention of the failure during the drawing process.

• Atmosphere
• /
• v.23 no.1
• /
• pp.33-37
• /
• 2013

In meteorology, exploitation of Kalman filter as a data assimilation system is virtually impossible due to simultaneous requirements of adjoint model and large computer resource. The other substitute of utilizing ensemble Kalman filter is only affordable by compensating an enormous usage of computing resource. Furthermore, the latter employs ensemble integration sets for evolving the background error covariance matrix by compensating the dynamical feature of the temporal evolution of weather conditions. We propose a new implementation method that works without the adjoint model by utilizing the explicit expression of the background error covariance matrix in backward evolution. It will also break a barrier in the evolution of the covariance matrix. The method may be applied with a slight modification to the real time assimilation or the retrospective analysis.

• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.497-502
• /
• 2004

This paper presents applications of the objective stress rates to stress update algorithms for transient shell dynamic analysis within the context of explicit time integration. The hypo elasto-plastic materials are assumed in establishing constitutive equations. The derivation of the objective stress rates are investigated by use of the Lie derivative. Comparison results are given between the Kirchhoff and Cauchy stress formulation. The Jacobian determination algorithm proposed in this paper is presented in association with the Belytschko-Lin-Tsay shell theory. Several numerical examples are demonstrated including contact and non-contact examples, by which proposed algorithms are compared with respect to the accuracy and effectiveness.

• Journal of Korean Society of Water and Wastewater
• /
• v.31 no.6
• /
• pp.511-519
• /
• 2017

Multi-regional water supply system, which installed for supplying multiple water demands, is characterized by large-sized, long-distance, tree-type layout. This system is vulnerable to long-standing service interruption when a pipe breaks is occurred. In this study, a numerical method is proposed to calculate drainage time that directly affects time of service interruption. To begin with, governing equations are formulated to embed the delayed drainage effect by the friction loss, and to resolve complicated connection of pipelines, which are derived from the continuity and energy equations. The nonlinear hydraulic equations are solved by using explicit time integration method and the Newton-Raphson method. The developed model is verified by comparing the result with analytical solution. Furthermore, the model's applicability is validated by the examples of pipelines in serial, in parallel, and complex layout. Finally, the model is utilized to suggest an appropriate actions to reduce the deviation of draining time in the C transmission line of the B multi-regional water supply system.