Pub Date : 2016-09-25DOI: 10.12941/JKSIAM.2016.20.175
Jaeseong Jang, C. Ahn
Ultrasound imaging is a widely used tool for visualizing human body’s internal organs and quantifying clinical parameters. Due to its advantages such as safety, noninvasiveness, portability, low cost and real-time 2D/3D imaging, diagnostic ultrasound industry has steadily grown. Since the technology advancements such as digital beam-forming, Doppler ultrasound, real-time 3D imaging and automated diagnosis techniques, there are still a lot of demands for image quality improvement, faster and accurate imaging, 3D color Doppler imaging and advanced functional imaging modes. In order to satisfy those demands, mathematics should be used properly and effectively in ultrasound imaging. Mathematics has been used commonly as mathematical modelling, numerical solutions and visualization, combined with science and engineering. In this article, we describe a brief history of ultrasound imaging, its basic principle, its applications in obstetrics/gynecology, cardiology and radiology, domestic-industrial products, contributions of mathematics and challenging issues in ultrasound imaging.
{"title":"INDUSTRIAL MATHEMATICS IN ULTRASOUND IMAGING","authors":"Jaeseong Jang, C. Ahn","doi":"10.12941/JKSIAM.2016.20.175","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.175","url":null,"abstract":"Ultrasound imaging is a widely used tool for visualizing human body’s internal organs and quantifying clinical parameters. Due to its advantages such as safety, noninvasiveness, portability, low cost and real-time 2D/3D imaging, diagnostic ultrasound industry has steadily grown. Since the technology advancements such as digital beam-forming, Doppler ultrasound, real-time 3D imaging and automated diagnosis techniques, there are still a lot of demands for image quality improvement, faster and accurate imaging, 3D color Doppler imaging and advanced functional imaging modes. In order to satisfy those demands, mathematics should be used properly and effectively in ultrasound imaging. Mathematics has been used commonly as mathematical modelling, numerical solutions and visualization, combined with science and engineering. In this article, we describe a brief history of ultrasound imaging, its basic principle, its applications in obstetrics/gynecology, cardiology and radiology, domestic-industrial products, contributions of mathematics and challenging issues in ultrasound imaging.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"77 1","pages":"175-202"},"PeriodicalIF":0.6,"publicationDate":"2016-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82526190","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}
Pub Date : 2016-09-25DOI: 10.12941/JKSIAM.2016.20.243
M. S. Islam
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.
{"title":"A MASS LUMPING AND DISTRIBUTING FINITE ELEMENT ALGORITHM FOR MODELING FLOW IN VARIABLY SATURATED POROUS MEDIA","authors":"M. S. Islam","doi":"10.12941/JKSIAM.2016.20.243","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.243","url":null,"abstract":"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.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"39 1","pages":"243-259"},"PeriodicalIF":0.6,"publicationDate":"2016-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73154702","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}
Pub Date : 2016-09-25DOI: 10.12941/JKSIAM.2016.20.203
M. Venkateswarlu, D. Lakshmi, K. N. Rao
The heat and mass transfer characteristics of the unsteady hydromagnetic natural convection flow with Hall current and Soret effect of an incompressible, viscous, electrically conducting, heat absorbing and optically thin radiating fluid flow past a suddenly started vertical infinite plate through fluid saturated porous medium in a rotating environment are taken into account in this paper. Derivations of exact analytical solutions are aimed under different physical properties. The velocity, concentration and temperature profiles, Sherwood number and Nusselt number are easily examined and discussed via the closed forms obtained. Soret effect and permeability parameter tends to accelerate primary and secondary fluid velocities whereas hall current, radiation and heat absorption have reverse effect on it. Radiation and heat absorption have tendency to enhance rate of heat transfer at the plate. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection fluid flow problems.
{"title":"SORET, HALL CURRENT, ROTATION, CHEMICAL REACTION AND THERMAL RADIATION EFFECTS ON UNSTEADY MHD HEAT AND MASS TRANSFER NATURAL CONVECTION FLOW PAST AN ACCELERATED VERTICAL PLATE","authors":"M. Venkateswarlu, D. Lakshmi, K. N. Rao","doi":"10.12941/JKSIAM.2016.20.203","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.203","url":null,"abstract":"The heat and mass transfer characteristics of the unsteady hydromagnetic natural convection flow with Hall current and Soret effect of an incompressible, viscous, electrically conducting, heat absorbing and optically thin radiating fluid flow past a suddenly started vertical infinite plate through fluid saturated porous medium in a rotating environment are taken into account in this paper. Derivations of exact analytical solutions are aimed under different physical properties. The velocity, concentration and temperature profiles, Sherwood number and Nusselt number are easily examined and discussed via the closed forms obtained. Soret effect and permeability parameter tends to accelerate primary and secondary fluid velocities whereas hall current, radiation and heat absorption have reverse effect on it. Radiation and heat absorption have tendency to enhance rate of heat transfer at the plate. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection fluid flow problems.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"31 1","pages":"203-224"},"PeriodicalIF":0.6,"publicationDate":"2016-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83165586","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}
Pub Date : 2016-09-25DOI: 10.12941/JKSIAM.2016.20.261
K. Parand, M. Delkhosh
In this paper, an integro-differential equation which arises in oscillating magnetic fields is studied. The generalized fractional order Chebyshev orthogonal functions (GFCF) collocation method used for solving this integral equation. The GFCF collocation method can be used in applied physics, applied mathematics, and engineering applications. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity, and efficiency of this method. The present method is converging and the error decreases with increasing collocation points.
{"title":"NUMERICAL SOLUTION OF AN INTEGRO-DIFFERENTIAL EQUATION ARISING IN OSCILLATING MAGNETIC FIELDS","authors":"K. Parand, M. Delkhosh","doi":"10.12941/JKSIAM.2016.20.261","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.261","url":null,"abstract":"In this paper, an integro-differential equation which arises in oscillating magnetic fields is studied. The generalized fractional order Chebyshev orthogonal functions (GFCF) collocation method used for solving this integral equation. The GFCF collocation method can be used in applied physics, applied mathematics, and engineering applications. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity, and efficiency of this method. The present method is converging and the error decreases with increasing collocation points.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"11 1","pages":"261-275"},"PeriodicalIF":0.6,"publicationDate":"2016-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81258425","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}
Pub Date : 2016-06-25DOI: 10.12941/JKSIAM.2016.20.123
Kyu-Hwan Jang, Min-Ku Lee
This article deals with the pricing of Asian options under a constant elasticity of variance (CEV) model as well as a stochastic elasticity of variance (SEV) model. The CEV and SEV models are underlying asset price models proposed to overcome shortcomings of the constant volatility model. In particular, the SEV model is attractive because it can characterize the feature of volatility in risky situation such as the global financial crisis both quantitatively and qualitatively. We use an asymptotic expansion method to approximate the no-arbitrage price of an arithmetic average Asian option under both CEV and SEV models. Subsequently, the zero and non-zero constant leverage effects as well as stochastic leverage effects are compared with each other. Lastly, we investigate the SEV correction effects to the CEV model for the price of Asian options.
{"title":"ARITHMETIC AVERAGE ASIAN OPTIONS WITH STOCHASTIC ELASTICITY OF VARIANCE","authors":"Kyu-Hwan Jang, Min-Ku Lee","doi":"10.12941/JKSIAM.2016.20.123","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.123","url":null,"abstract":"This article deals with the pricing of Asian options under a constant elasticity of variance (CEV) model as well as a stochastic elasticity of variance (SEV) model. The CEV and SEV models are underlying asset price models proposed to overcome shortcomings of the constant volatility model. In particular, the SEV model is attractive because it can characterize the feature of volatility in risky situation such as the global financial crisis both quantitatively and qualitatively. We use an asymptotic expansion method to approximate the no-arbitrage price of an arithmetic average Asian option under both CEV and SEV models. Subsequently, the zero and non-zero constant leverage effects as well as stochastic leverage effects are compared with each other. Lastly, we investigate the SEV correction effects to the CEV model for the price of Asian options.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"60 1","pages":"123-135"},"PeriodicalIF":0.6,"publicationDate":"2016-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81649358","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}
Pub Date : 2016-06-25DOI: 10.12941/JKSIAM.2016.20.137
Kwang-Yeon Kim
In this paper we analyze an a posteriori error estimator based on flux recovery for lowest-order finite element discretizations of elliptic interface problems. The flux recovery considered here is based on averaging the discrete normal fluxes and/or tangential derivatives at midpoints of edges with weight factors adapted to discontinuous coefficients. It is shown that the error estimator based on this flux recovery is equivalent to the error estimator of Bernardi and Verfurth based on the standard edge residuals uniformly with respect to jumps of the coefficient between subdomains. Moreover, as a byproduct, we obtain slightly modified weight factors in the edge residual estimator which are expected to produce more accurate results.
{"title":"ROBUST A POSTERIORI ERROR ESTIMATOR FOR LOWEST-ORDER FINITE ELEMENT METHODS OF INTERFACE PROBLEMS","authors":"Kwang-Yeon Kim","doi":"10.12941/JKSIAM.2016.20.137","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.137","url":null,"abstract":"In this paper we analyze an a posteriori error estimator based on flux recovery for lowest-order finite element discretizations of elliptic interface problems. The flux recovery considered here is based on averaging the discrete normal fluxes and/or tangential derivatives at midpoints of edges with weight factors adapted to discontinuous coefficients. It is shown that the error estimator based on this flux recovery is equivalent to the error estimator of Bernardi and Verfurth based on the standard edge residuals uniformly with respect to jumps of the coefficient between subdomains. Moreover, as a byproduct, we obtain slightly modified weight factors in the edge residual estimator which are expected to produce more accurate results.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"14 1","pages":"137-150"},"PeriodicalIF":0.6,"publicationDate":"2016-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87118684","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}
Pub Date : 2016-06-25DOI: 10.12941/JKSIAM.2016.20.107
Y. Park, Jaehyun Park
We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and Lovasz as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of O(N 4 logB) multiplications (or, O(N 5 (logB) 2 ) bit operations) for a lattice basis matrix H(∈ R M×N ) where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm’s complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.
{"title":"ANALYSIS OF THE UPPER BOUND ON THE COMPLEXITY OF LLL ALGORITHM","authors":"Y. Park, Jaehyun Park","doi":"10.12941/JKSIAM.2016.20.107","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.107","url":null,"abstract":"We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and Lovasz as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of O(N 4 logB) multiplications (or, O(N 5 (logB) 2 ) bit operations) for a lattice basis matrix H(∈ R M×N ) where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm’s complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"11 1","pages":"107-121"},"PeriodicalIF":0.6,"publicationDate":"2016-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74308223","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}
Pub Date : 2016-06-25DOI: 10.12941/JKSIAM.2016.20.163
Junseok Kim, Minhyun Yoo, Hyeju Son, Seunggyu Lee, M. Kim, Yongho Choi, Darae Jeong, Young Rock Kim
In this paper, we propose an optimal choice scheme to determine the best option among comparable options whose current expectations are all the same under the condition that an investor has a confidence in the future value realization of underlying assets. For this purpose, we use a path-averaged option as our base instrument in which we calculate the time discounted value along the path and divide it by the number of time steps for a given expected path. First, we consider three European call options such as vanilla, cash-or-nothing, and asset-or-nothing as our comparable set of choice schemes. Next, we perform the experiments using historical data to prove the usefulness of our proposed scheme. The test suggests that the path-averaged option value is a good guideline to choose an optimal option.
{"title":"PATH AVERAGED OPTION VALUE CRITERIA FOR SELECTING BETTER OPTIONS","authors":"Junseok Kim, Minhyun Yoo, Hyeju Son, Seunggyu Lee, M. Kim, Yongho Choi, Darae Jeong, Young Rock Kim","doi":"10.12941/JKSIAM.2016.20.163","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.163","url":null,"abstract":"In this paper, we propose an optimal choice scheme to determine the best option among comparable options whose current expectations are all the same under the condition that an investor has a confidence in the future value realization of underlying assets. For this purpose, we use a path-averaged option as our base instrument in which we calculate the time discounted value along the path and divide it by the number of time steps for a given expected path. First, we consider three European call options such as vanilla, cash-or-nothing, and asset-or-nothing as our comparable set of choice schemes. Next, we perform the experiments using historical data to prove the usefulness of our proposed scheme. The test suggests that the path-averaged option value is a good guideline to choose an optimal option.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"9 4 1","pages":"163-174"},"PeriodicalIF":0.6,"publicationDate":"2016-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78500247","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}
Pub Date : 2016-06-25DOI: 10.12941/JKSIAM.2016.20.151
Sungchul Bae, Y. Ahn
In this paper, we present a C 3 quartic B-spline approximation of circular arcs. The Hausdorff distance between the C 3 quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the C 3 quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the C 3 quartic B-spline approximation of a circular arc is also presented.
{"title":"APPROXIMATION ORDER OF C 3 QUARTIC B-SPLINE APPROXIMATION OF CIRCULAR ARC","authors":"Sungchul Bae, Y. Ahn","doi":"10.12941/JKSIAM.2016.20.151","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.151","url":null,"abstract":"In this paper, we present a C 3 quartic B-spline approximation of circular arcs. The Hausdorff distance between the C 3 quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the C 3 quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the C 3 quartic B-spline approximation of a circular arc is also presented.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"69 1","pages":"151-161"},"PeriodicalIF":0.6,"publicationDate":"2016-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84304414","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}
Pub Date : 2016-03-25DOI: 10.12941/JKSIAM.2016.20.037
M. S. I. Mallik, Md.Ashraf Uddin
A large eddy simulation (LES) of a turbulent channel flow is performed by using the third order low-storage Runge–Kutta method in time and second order finite difference formulation in space with staggered grid at a Reynolds number, Re τ = 590 based on the channel half width, δ and wall shear velocity, u τ . To reduce the calculation cost of LES, algebraic wall model (AWM) is applied to approximate the near-wall region. The computation is performed in a domain of 2πδ×2δ×πδ with 32×20×32 grid points. Standard Smagorinsky model is used for subgrid-scale (SGS) modeling. Essential turbulence statistics of the flow field are computed and compared with Direct Numerical Simulation (DNS) data and LES data using no wall model. Agreements as well as discrepancies are discussed. The flow structures in the computed flow field have also been discussed and compared with LES data using no wall model.
{"title":"LARGE EDDY SIMULATION OF TURBULENT CHANNEL FLOW USING ALGEBRAIC WALL MODEL","authors":"M. S. I. Mallik, Md.Ashraf Uddin","doi":"10.12941/JKSIAM.2016.20.037","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.037","url":null,"abstract":"A large eddy simulation (LES) of a turbulent channel flow is performed by using the third order low-storage Runge–Kutta method in time and second order finite difference formulation in space with staggered grid at a Reynolds number, Re τ = 590 based on the channel half width, δ and wall shear velocity, u τ . To reduce the calculation cost of LES, algebraic wall model (AWM) is applied to approximate the near-wall region. The computation is performed in a domain of 2πδ×2δ×πδ with 32×20×32 grid points. Standard Smagorinsky model is used for subgrid-scale (SGS) modeling. Essential turbulence statistics of the flow field are computed and compared with Direct Numerical Simulation (DNS) data and LES data using no wall model. Agreements as well as discrepancies are discussed. The flow structures in the computed flow field have also been discussed and compared with LES data using no wall model.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"5 1","pages":"37-50"},"PeriodicalIF":0.6,"publicationDate":"2016-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89917950","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}
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