• Journal of Ocean Engineering and Technology
• /
• v.14 no.1
• /
• pp.1-5
• /
• 2000

A numerical analysis for wave motion in the shallow water is presented. The method is based on potential theory. The fully nonlinear free surface boundary condition is assumed in an inner domain and this solution is matched along an assumed common boundary to a linear solution in outer domain. In two-dimensional problem Cauchy's integral theorem is applied to calculate the complex potential and its time derivative along boundary.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.3 no.1
• /
• pp.20-26
• /
• 2011

A weakly nonlinear seakeeping methodology for predicting motions and loads is presented in this paper. This methodology assumes linear radiation and diffraction forces, calculated in the frequency domain, and fully nonlinear Froude-Krylov and hydrostatic forces, evaluated in the time domain. The particular approach employed here allows to overcome numerical problems connected to the determination of the impulse response functions. The procedure is divided into three consecutive steps: evaluation of dynamic sinkage and trim in calm water that can significantly influence the final results, a linear seakeeping analysis in the frequency domain and a weakly nonlinear simulation. The first two steps are performed employing a three-dimensional Rankine panel method. Nonlinear Froude-Krylov and hydrostatic forces are computed in the time domain by pressure integration on the actual wetted surface at each time step. Although nonlinear forces are evaluated into the time domain, the equations of motion are solved in the frequency domain iteratively passing from the frequency to the time domain until convergence. The containership S175 is employed as a test case for evaluating the capability of this methodology to correctly predict the nonlinear behavior related to wave induced motions and loads in head seas; numerical results are compared with experimental data provided in literature.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.3
• /
• pp.243-259
• /
• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• Journal of applied mathematics & informatics
• /
• v.4 no.1
• /
• pp.17-30
• /
• 1997

In this work we approximate the solution of initialboun-dary value problem using a Galerkin-finite element method for the spatial discretization and Implicit Runge-Kutta method for the spatial discretization and implicit Runge-Kutta methods for the time stepping. To deal with the nonlinear term f(x, t, u), we introduce the well-known extrapolation sheme which was used widely to prove the convergence in $L_2$-norm. We present computational results showing that the optimal order of convergence arising under $L_2$-norm will be preserved in $L_{\infty}$-norm.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.355-379
• /
• 2024

In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.

• Journal of Ocean Engineering and Technology
• /
• v.17 no.6
• /
• pp.7-15
• /
• 2003

A Digital Wave Tank simulation technique, based on a finite-difference method and a modified marker-and-cell (MAC) algorithm, is applied in order to investigate the characteristics of nonlinear Tsunami propagations and their interactions with a 2D sloping beach, Ohkushiri Island, and to predict maximum wove run-up around the island. The Navier-Stokes (NS) and continuity equation are governed in the computational domain, and the boundary values are updated at each time step, by a finite-difference time-marching scheme in the frame of the rectangular coordinate system. The fully nonlinear, kinematic, free-surface condition is satisfied by the modified marker-density function technique. The near shore Tsunami is assumed to be a solitary wave, and is generated from the numerical wave-maker in the developed Digital Wave Tank. The simulation results are compared with the experiments and other numerical methods, based on the shallow-water wave theory.

• Smart Structures and Systems
• /
• v.5 no.5
• /
• pp.507-515
• /
• 2009

The present work is an alternative methodology in order to balance a nonlinear highly flexible rotor by using neural networks. This procedure was developed aiming at improving the performance of classical balancing methods, which are developed in the context of linearity between acting forces and resulting displacements and are not well adapted to these situations. In this paper a fully experimental procedure using neural networks is implemented for dealing with the adaptive balancing of nonlinear rotors. The nonlinearity results from the large displacements measured due to the high flexibility of the foundation. A neural network based meta-model was developed to represent the system. The initialization of the learning procedure of the network is performed by using the influence coefficient method and the adaptive balancing strategy is prone to converge rapidly to a satisfactory solution. The methodology is tested successfully experimentally.

• International Journal of Control, Automation, and Systems
• /
• v.4 no.3
• /
• pp.302-307
• /
• 2006

The aim of applying Functional Electrical Stimulation (FES) is to restore a person's motor function by directly supplying the controlled electrical currents to the site of the paralyzed muscles. However, most clinically utilized FES systems have adapted an open-loop control scheme. Recently the closed-loop control scheme has been considered for setting up the FES system, but due to the inherent nonlinearities in the musculoskeletal system, the nonlinearities were not fully compensated and it caused the oscillatory responses for tracking the output variables. In this study, a nonlinear controller model that has two inverse compensation units is proposed with the compromising feedback linearization method and this will eventually be used to design the FES control system for stimulating a knee joint musculoskeletal system.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
• /
• 2003.05a
• /
• pp.231-239
• /
• 2003

A Digital Wave Tank simulation technique based on a finite-difference method and a modified marker-and-cell (MAC) algorithm is applied to investigate the characteristics of nonlinear Tsunami propagations and their interactions with a 2D sloping beach and Ohkushiri island, and to predict maximum wave run-up around the island. The Navier-Stokes (NS) and continuity equation are governed in the computational domain and the boundary values updated at each time step by a finite-difference time-marching scheme in the frame of rectangular coordinate system. The fully nonlinear kinematic free-surface condition is satisfied by the modified marker-density function technique. The Nearshore Tsunami is assumed to be a solitary wave and generated from the numerical wavemaker in the developed Digital Wave Tank. The simulation results are compared with the experiments and other numerical methods based on the shallow-water wave theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.18 no.4
• /
• pp.337-350
• /
• 2014

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.