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NUMERICAL IMPLEMENTATION OF THE TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER–STOKES EQUATION 二维不可压缩navier-stokes方程的数值实现
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-06-25 DOI: 10.12941/JKSIAM.2015.19.103
Yongho Choi, Darae Jeong, Seunggyu Lee, Junseok Kim
{"title":"NUMERICAL IMPLEMENTATION OF THE TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER–STOKES EQUATION","authors":"Yongho Choi, Darae Jeong, Seunggyu Lee, Junseok Kim","doi":"10.12941/JKSIAM.2015.19.103","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.103","url":null,"abstract":"In this paper, we briefly review and describe a projection algorithm for numerically computing the two-dimensional time-dependent incompressible Navier?Stokes equation. The projection method, which was originally introduced by Alexandre Chorin [A.J. Chorin, Numerical solution of the Navier?Stokes equations, Math. Comput., 22 (1968), pp. 745?762], is an effective numerical method for solving time-dependent incompressible fluid flow problems. The key advantage of the projection method is that we do not compute the momentum and the continuity equations at the same time, which is computationally difficult and costly. In the projection method, we compute an intermediate velocity vector field that is then projected onto divergence-free fields to recover the divergence-free velocity. Numerical solutions for flows inside a driven cavity are presented. We also provide the source code for the programs so that interested readers can modify the programs and adapt them for their own purposes.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82430256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
NOTE ON LOCAL BOUNDEDNESS FOR WEAK SOLUTIONS OF NEUMANN PROBLEM FOR SECOND-ORDER ELLIPTIC EQUATIONS 二阶椭圆型方程neumann问题弱解的局部有界性
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-06-25 DOI: 10.12941/JKSIAM.2015.19.189
Seick Kim
{"title":"NOTE ON LOCAL BOUNDEDNESS FOR WEAK SOLUTIONS OF NEUMANN PROBLEM FOR SECOND-ORDER ELLIPTIC EQUATIONS","authors":"Seick Kim","doi":"10.12941/JKSIAM.2015.19.189","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.189","url":null,"abstract":"The goal of this note is to provide a detailed proof for local boundedness estimate near the boundary for weak solutions for second order elliptic equations with bounded measurable coefficients subject to Neumann boundary condition.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88610814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
CONSEQUENCE OF BACKWARD EULER AND CRANK-NICOLSOM TECHNIQUES IN THE FINITE ELEMENT MODEL FOR THE NUMERICAL SOLUTION OF VARIABLY SATURATED FLOW PROBLEMS 后向欧拉和曲克-尼克索姆技术在变饱和流动问题有限元模型数值解中的应用
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-06-25 DOI: 10.12941/JKSIAM.2015.19.197
M. S. Islam
{"title":"CONSEQUENCE OF BACKWARD EULER AND CRANK-NICOLSOM TECHNIQUES IN THE FINITE ELEMENT MODEL FOR THE NUMERICAL SOLUTION OF VARIABLY SATURATED FLOW PROBLEMS","authors":"M. S. Islam","doi":"10.12941/JKSIAM.2015.19.197","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.197","url":null,"abstract":"Modeling water flow in variably saturated, porous media is important in many branches of science and engineering. Highly nonlinear relationships between water content and hydraulic conductivity and soil-water pressure result in very steep wetting fronts causing numerical problems. These include poor efficiency when modeling water infiltration into very dry porous media, and numerical oscillation near a steep wetting front. A one-dimensional finite element formulation is developed for the numerical simulation of variably saturated flow systems. First order backward Euler implicit and second order Crank?Nicolson time discretization schemes are adopted as a solution strategy in this formulation based on Picard and Newton iterative techniques. Five examples are used to investigate the numerical performance of two approaches and the different factors are highlighted that can affect their convergence and efficiency. The first test case deals with sharp moisture front that infiltrates into the soil column. It shows the capability of providing a mass-conservative behavior. Saturated conditions are not developed in the second test case. Involving of dry initial condition and steep wetting front are the main numerical complexity of the third test example. Fourth test case is a rapid infiltration of water from the surface, followed by a period of redistribution of the water due to the dynamic boundary condition. The last one-dimensional test case involves flow into a layered soil with variable initial conditions. The numerical results indicate that the Crank?Nicolson scheme is inefficient compared to fully implicit backward Euler scheme for the layered soil problem but offers same accuracy for the other homogeneous soil cases.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82798912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
NUMERICAL SOLUTIONS OF BURGERS EQUATION BY REDUCED-ORDER MODELING BASED ON PSEUDO-SPECTRAL COLLOCATION METHOD 基于伪谱配置法的burgers方程的降阶建模数值解
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-06-25 DOI: 10.12941/JKSIAM.2015.19.123
Jeong-Kweon Seo, B. Shin
{"title":"NUMERICAL SOLUTIONS OF BURGERS EQUATION BY REDUCED-ORDER MODELING BASED ON PSEUDO-SPECTRAL COLLOCATION METHOD","authors":"Jeong-Kweon Seo, B. Shin","doi":"10.12941/JKSIAM.2015.19.123","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.123","url":null,"abstract":"In this paper, a reduced-order modeling(ROM) of Burgers equations is studied based on pseudo-spectral collocation method. A ROM basis is obtained by the proper orthogonal decomposition(POD). Crank-Nicolson scheme is applied in time discretization and the pseudo-spectral element collocation method is adopted to solve linearlized equation based on the Newton method in spatial discretization. We deliver POD-based algorithm and present some numerical experiments to show the efficiency of our proposed method.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87054032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
RADIATION EFFECTS ON MHD BOUNDARY LAYER FLOW OF LIQUID METAL OVER A POROUS STRETCHING SURFACE IN POROUS MEDIUM WITH HEAT GENERATION 辐射对多孔介质中液态金属在多孔拉伸表面上流动的影响
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-03-25 DOI: 10.12941/JKSIAM.2015.19.083
M. Venkateswarlu, G. Reddy, D. Lakshmi
{"title":"RADIATION EFFECTS ON MHD BOUNDARY LAYER FLOW OF LIQUID METAL OVER A POROUS STRETCHING SURFACE IN POROUS MEDIUM WITH HEAT GENERATION","authors":"M. Venkateswarlu, G. Reddy, D. Lakshmi","doi":"10.12941/JKSIAM.2015.19.083","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.083","url":null,"abstract":"The present paper analyses the radiation effects of mass transfer on steady nonlinear MHD boundary layer flow of a viscous incompressible fluid over a nonlinear porous stretching surface in a porous medium in presence of heat generation. The liquid metal is assumed to be gray, emitting, and absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations are solved numerically using Runge?Kutta fourth order method along with shooting technique. Comparison with previously published work is obtained and good agreement is found. The effects of various governing parameters on the liquid metal fluid dimensionless velocity, dimensionless temperature, dimensionless concentration, skin-friction coefficient, Nusselt number and Sherwood number are discussed with the aid of graphs.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86575354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
A MULTIVARIATE JUMP DIFFUSION PROCESS FOR COUNTERPARTY RISK IN CDS RATES CDS利率中交易对手风险的多变量跳跃扩散过程
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-03-25 DOI: 10.12941/JKSIAM.2015.19.023
S. Ramli, Jiwook Jang
{"title":"A MULTIVARIATE JUMP DIFFUSION PROCESS FOR COUNTERPARTY RISK IN CDS RATES","authors":"S. Ramli, Jiwook Jang","doi":"10.12941/JKSIAM.2015.19.023","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.023","url":null,"abstract":"We consider counterparty risk in CDS rates. To do so, we use a multivariate jump diffusion process for obligors’ default intensity, where jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process. We apply copuladependent default intensities of multivariate Cox process to derive the joint Laplace transform that provides us with joint survival/default probability and other relevant joint probabilities. For that purpose, the piecewise deterministic Markov process (PDMP) theory developed in [7] and the martingale methodology in [6] are used. We compute survival/default probability using three copulas, which are Farlie-Gumbel-Morgenstern (FGM), Gaussian and Student-t copulas, with exponential marginal distributions. We then apply the results to calculate CDS rates assuming deterministic rate of interest and recovery rate. We also conduct sensitivity analysis for the CDS rates by changing the relevant parameters and provide their figures.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73097399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
FINITE-DIFFERENCE BISECTION ALGORITHMS FOR FREE BOUNDARIES OF AMERICAN OPTIONS 美式期权自由边界的有限差分等分算法
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-03-25 DOI: 10.12941/JKSIAM.2015.19.001
Sunbu Kang, Taekkeun Kim, YongHoon Kwon
{"title":"FINITE-DIFFERENCE BISECTION ALGORITHMS FOR FREE BOUNDARIES OF AMERICAN OPTIONS","authors":"Sunbu Kang, Taekkeun Kim, YongHoon Kwon","doi":"10.12941/JKSIAM.2015.19.001","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.001","url":null,"abstract":"This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r ＞ d, r ≤ d, long-time or short-time maturity T.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81788427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
MATHEMATICAL MODELLING AND ITS SIMULATION OF A QUASI-STATIC THERMOELASTIC PROBLEM IN A SEMI-INFINITE HOLLOW CIRCULAR DISK DUE TO INTERNAL HEAT GENERATION 半无限中空圆盘内热产生的准静态热弹性问题的数学建模与模拟
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-03-25 DOI: 10.12941/JKSIAM.2015.19.069
K. Gaikwad
{"title":"MATHEMATICAL MODELLING AND ITS SIMULATION OF A QUASI-STATIC THERMOELASTIC PROBLEM IN A SEMI-INFINITE HOLLOW CIRCULAR DISK DUE TO INTERNAL HEAT GENERATION","authors":"K. Gaikwad","doi":"10.12941/JKSIAM.2015.19.069","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.069","url":null,"abstract":"The present paper deals with the determination of temperature, displacement and thermal stresses in a semi-infinite hollow circular disk due to internal heat generation within it. Initially the disk is kept at arbitrary temperature F(r, z). For times t ＞ 0 heat is generated within the circular disk at a rate of g(r, z, t) Btu/hr.ft³. The heat flux is applied on the inner circular boundary (r = a) and the outer circular boundary (r = b). Also, the lower surface (z = 0) is kept at temperature Q₃(r, t) and the upper surface (z = ∞) is kept at zero temperature. Hollow circular disk extends in the z-direction from z = 0 to infinity. The governing heat conduction equation has been solved by using finite Hankel transform and the generalized finite Fourier transform. As a special case mathematical model is constructed for different metallic disk have been considered. The results are obtained in series form in terms of Bessel’s functions. These have been computed numerically and illustrated graphically.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89471374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A MODIFIED CAHN-HILLIARD EQUATION FOR 3D VOLUME RECONSTRUCTION FROM TWO PLANAR CROSS SECTIONS 二维平面截面三维体积重建的修正cahn-hilliard方程
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-03-25 DOI: 10.12941/JKSIAM.2015.19.047
Seunggyu Lee, Yongho Choi, Doyoon Lee, Hong-Kwon Jo, Seung Hyun Lee, S. Myung, Junseok Kim
{"title":"A MODIFIED CAHN-HILLIARD EQUATION FOR 3D VOLUME RECONSTRUCTION FROM TWO PLANAR CROSS SECTIONS","authors":"Seunggyu Lee, Yongho Choi, Doyoon Lee, Hong-Kwon Jo, Seung Hyun Lee, S. Myung, Junseok Kim","doi":"10.12941/JKSIAM.2015.19.047","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.047","url":null,"abstract":"In this paper, we present an implicit method for reconstructing a 3D solid model from two 2D cross section images. The proposed method is based on the Cahn-Hilliard model for the image inpainting. Image inpainting is the process of reconstructing lost parts of im- ages based on information from neighboring areas. We treat the empty region between the two cross sections as inpainting region and use two cross sections as neighboring information. We initialize the empty region by the linear interpolation. We perform numerical experiments demonstrating that our proposed method can generate a smooth 3D solid model from two cross section data.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86843569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
COUETTE FLOW OF TWO IMMISCIBLE LIQUIDS BETWEEN TWO PARALLEL POROUS PLATES IN A ROTATING CHANNEL 两种不混溶液体在旋转通道中两个平行多孔板之间的库埃特流动
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-03-25 DOI: 10.12941/JKSIAM.2015.19.057
Ch. Baby Rani
{"title":"COUETTE FLOW OF TWO IMMISCIBLE LIQUIDS BETWEEN TWO PARALLEL POROUS PLATES IN A ROTATING CHANNEL","authors":"Ch. Baby Rani","doi":"10.12941/JKSIAM.2015.19.057","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.057","url":null,"abstract":"When a straight channel formed by two parallel porous plates, through which two immiscible liquids occupying different heights are flowing a secondary motion is set up. The motion is caused by moving the upper plate with a uniform velocity about an axis perpendicular to the plates. The solutions are exact solutions. Here we discuss the effect of suction parameter and the position of interface on the flow phenomena in case of Couette flow. The velocity distributions for the primary and secondary flows have been discussed and presented graphically. The skin-friction amplitude at the upper and lower plates has been discussed for various physical parameters.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2015-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72546460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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