{"title":"Multigrid solution of non‐linear balance equations in meteorology","authors":"S. Fulton","doi":"10.1002/CNM.1630081001","DOIUrl":"https://doi.org/10.1002/CNM.1630081001","url":null,"abstract":"Multigrid algorithms are presented for several elliptic problems arising in models of balanced atmospheric dynamics. The equations are generalizations of the Monge—Ampere equation and are non-linear in the highest-order terms. The problem formulation is reviewed, along with a method of dealing with a lower boundary which is not a co-ordinate surface, and details of the discretization and relaxation are given. Numerical results from two- and three-dimensional problems show the accuracy and efficiency of the method.","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"2013 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128131776","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}
{"title":"A multigrid method for solution of vorticity—velocity form of 3‐D navier—stokes equations","authors":"Y. Huang, U. Ghia","doi":"10.1002/CNM.1630081002","DOIUrl":"https://doi.org/10.1002/CNM.1630081002","url":null,"abstract":"A multigrid method has been developed and applied to the simulation of unsteady three-dimensional incompressible flow, using the Navier—Stokes equations in terms of vorticity and velocity variables. A system of equations for the velocity problem, consisting of the continuity equation and three curl equations, is first formulated as a uniquely determined, non-singular system. An efficient and robust technique, namely the multigrid distributive Gauss—Seidel scheme, is developed for solution of this system of algebraic equations. The method is applied to study 3-D flow in a shear-driven cavity.","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115358283","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}
{"title":"Efficient computation of inviscid flow fields around complex configurations using a multiblock multigrid method","authors":"C. Rossow","doi":"10.1002/CNM.1630081004","DOIUrl":"https://doi.org/10.1002/CNM.1630081004","url":null,"abstract":"The efficient implementation of a multigrid technique for use on block-structured, body-fitted meshes is investigated. The algorithm employed for the solution of inviscid flow fields uses central differences with artificial dissipation, and time integration is performed by a five-stage Runge—Kutta scheme. A major point of concern is the amount of work which may be performed within a block before switching to the next block. In this study three different strategies are under consideration. In the first strategy data are exchanged between blocks in each stage of the Runge—Kutta time-stepping scheme. This keeps a possible time lag between blocks to a minimum, but requires a large amount of I/O operations and storage. The second strategy performs a complete Runge—Kutta cycle within a block before switching to the next. Having completed one time step in all blocks, a second sweep through all blocks is done in order to evaluate residuals necessary for the restriction to coarser meshes. In the third strategy both a complete Runge—Kutta cycle and the residual evaluation for the restriction operator are done within a block, allowing a minimum of I/O and storage. A primary application of all three strategies to a two-block mesh around a wing-body combination showed no significant differences in the convergence of the multigrid algorithm. To investigate the impact of the different strategies on complex configurations, computations were carried out on an 11-block mesh around a wing-body—engine-pylon configuration. Both the first and second strategies delivered converged results, but the third failed due to the larger time lag between blocks. Full multigrid was then used to obtain a preconditioned starting solution for the finest grid. This alleviated the time lag to such an extent that even the third strategy yielded convergence.","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129865672","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}
{"title":"Application of PLTMG to a stream function problem","authors":"J. Mooney","doi":"10.1002/CNM.1630080508","DOIUrl":"https://doi.org/10.1002/CNM.1630080508","url":null,"abstract":"The finite-element package PLTMG was designed to solve a wide variety of non-linear, scalar elliptic PDEs. In this paper we examine the application of PLTMG to the solution of a potential flow problem using the stream function formulation. The flow problem is that of irrotational steady flow through a shallow lake with prescribed inflows and outflows. A two-dimensional (vertically integrated) model is used. One or more islands may be present. The paper focuses on the advantages of the stream function formulation for obtaining accurate streamlines and partial residence times as opposed to using a potential function formulation. If islands are present the stream values at the island boundaries are unknowns which must be determined to fulfil a condition of zero circulation round each island. Thus, if N islands are present, an N-fold linear continuation must be performed to determine the solution.","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122682519","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}
{"title":"A 3-D refinement algorithm suitable for adaptive and multi-grid techniques","authors":"M. Rivara, Cristian Levin","doi":"10.1002/CNM.1630080502","DOIUrl":"https://doi.org/10.1002/CNM.1630080502","url":null,"abstract":"A 3-D refinement algorithm for tetrahedral meshes is presented and discussed. An empirical study of the reduction of solid angle size due to repeated subdivisions has shown the algorithm to be in practice a powerful and reliable tool for mesh refinement suitable to be combined with adaptive finite-element methods and multi-grid algorithms.","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123483463","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}
{"title":"Adaptive mesh refinement for faceted shells","authors":"J. Bonet, A. Pica, J. Peiró, R. D. Wood","doi":"10.1002/CNM.1630080506","DOIUrl":"https://doi.org/10.1002/CNM.1630080506","url":null,"abstract":"The application of the Zienkiewicz and Zhu error estimator to three-dimensional faceted shells presents some difficulties which arise from the lack of C1 continuity of the geometry. This paper presents a method to circumvent such difficulties based on the existence of a mapping from a flat reference configuration to the actual shell. This mapping is used not only to enable meshes to be generated in a two-dimensional space, but also to define a stress measure – similar to the first Piola–Kirchhoff stress used in large deformation mechanics – which can be consistently smoothed over the reference configuration. A preliminary investigation of the method is provided by three simple examples.","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129567975","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}
{"title":"A new way to measure the accuracy of the BEM solution","authors":"X. Zhong","doi":"10.1002/CNM.1630080504","DOIUrl":"https://doi.org/10.1002/CNM.1630080504","url":null,"abstract":"","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128910431","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}
{"title":"Iterative techniques for non-linear eigenvalue buckling problems","authors":"A. Mirasso, L. Godoy","doi":"10.1002/CNM.1630080505","DOIUrl":"https://doi.org/10.1002/CNM.1630080505","url":null,"abstract":"Structural stability problems under displacement-dependent loads often take the form of non-linear eigenvalue problems in which the eigenvalue is raised to an exponent. Iterative techniques are considered in this work for the solution of non-linear eigenproblems of the form (K - λK1 - K2(λp))x = 0. The problem is linearized at each iteration using two alternative procedures: through updating the stiffness matrix K or else by updating the initial stress matrix. Numerical examples are used to illustrate the difficulties associated with the first technique, whereas it is shown that the second one yields better convergence rates than other existing techniques.","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115180530","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}
{"title":"On stress intensity factor computation from the quarter‐point element displacements","authors":"I. Lim, I. Johnston, S. Choi","doi":"10.1002/CNM.1630080503","DOIUrl":"https://doi.org/10.1002/CNM.1630080503","url":null,"abstract":"In conjunction with the quarter-point element, a wide range of stress intensity factor computation techniques may be employed. Of these, the displacement correlation technique (DCT) and the quarter-point displacement technique (QPDT) have been in common use. It has been suggested by various investigators that the DCT is more rational in formulation and should therefore be more accurate than the QPDT. However, published numerical studies provide conflicting results on the relative performance of either technique. To resolve this anomaly, this study provides a detailed investigation on the DCT and QPDT performance. On the basis of considering the second term in Westergaard's expression and supported by numerical experiments, it is concluded that the QPDT would generally perform better than the DCT.","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128754710","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}
{"title":"Note on sensitivity analysis to improve eigenvalue analysis","authors":"Lien-Wen Chen, D. Ku","doi":"10.1002/CNM.1630080507","DOIUrl":"https://doi.org/10.1002/CNM.1630080507","url":null,"abstract":"The stability behaviour of a cantilever beam, carrying a concentrated mass at the free end and subjected to a uniformly distributed follower force, is studied by the finite-element method. In the present finite-element formulation, the Timoshenko beam theory is utilized to derive the governing equations of motion. In order to more quickly and efficiently obtain the critical load for such a non-conservative system, a numerical technique which utilizes the eigenvalue sensitivity with respect to the follower force is introduced instead of the conventional trial-and-error technique. The high accuracy and rapid rate of convergence through the combination of the present finite-element model and the numerical algorithm are demonstrated with the numerical example given.","PeriodicalId":136398,"journal":{"name":"Communications in Applied Numerical Methods","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123693590","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}