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Accuracy analysis of immersed boundary method using method of manufactured solutions

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Applied Mathematics and Mechanics(English Edition) 2010年第10期31卷 1197-1208页

作者：宫兆新鲁传敬黄华雄 Department of Mechanics Shanghai Jiao Tong University State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University Department of Mathematics and Statistics York University

The immersed boundary method is an effective technique for modeling and simulating fluid-structure interactions especially in the area of *** paper analyzes the accuracy of the immersed boundary *** procedure contains two parts,i.e.,the code verification and the accuracy *** code verification provides the confidence that the code used is free of mistakes,and the accuracy analysis gives the order of accuracy of the immersed boundary *** method of manufactured solutions is taken as a means for both *** the first part,the numerical code employs a second-order discretization scheme,i.e.,it has second-order accuracy in *** matches the calculated order of accuracy obtained in the numerical calculation for all *** means that the code contains no mistake,which is a premise of the subsequent *** second part introduces a jump in the manufactured solution for the pressure and adds the corresponding singular forcing terms in the momentum *** analyzing the discretization errors,the accuracy of the immersed boundary method is proven to be first order even though the discretization scheme is second *** has been found that the coarser mesh may not be sensitive enough to capture the influence of the immersed boundary,and the refinement on the Lagrangian markers barely has any effect on the numerical calculation.

关键词： manufactured solution immersed boundary method order of accuracy code verification discretization error

Computational uncertainty principle in nonlinear ordinary differential equations——Ⅱ.Theoretical analysis

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Science China(Technological Sciences) 2001年第1期44卷 55-74页

作者：李建平曾庆存丑纪范 1. State Key Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG) Institute of Atmospheric Physics Chinese Academy of Sciences 100029 Beijing China 2. Department of Atmospheric Sciences Lanzhou University 730000 Lanzhou China

The error propagation for general numerical method in ordinarydifferential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components of round-off error occurring in floating-point computation are fully detailed. By introducing a new kind of recurrent inequality, the classical error bounds for linear multistep methods are essentially improved, and joining probabilistic theory the “normal” growth of accumulated round-off error is derived. Moreover, a unified estimate for the total error of general method is given. On the basis of these results, we rationally interpret the various phenomena found in the numerical experiments in part I of this paper and derive two universal relations which are independent of types of ODEs, initial values and numerical schemes and are consistent with the numerical results. Furthermore, we give the explicitly mathematical expression of the computational uncertainty principle and expound the intrinsic relation between two uncertainties which result from the inaccuracies of numerical method and calculating machine.

关键词： computational uncertainty principle round-off error discretization error universal relation ma-chine precision maximally effective computation time (MECT) optimal stepsize (OS) convergence.

Uncertainty Propagation of Structural Computation for Fatigue Assessment

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Journal of Marine Science and Application 2022年第4期21卷 55-66页

作者： Ludovic Mell Valentine Rey Franck Schoefs Benjamin Rocher Nantes Université École Centrale NantesCNRSGeMUMR 6183F-44000 NantesFrance Chantiers de l’Atlantique Avenue Bourdelle-CS90180St-Nazaire CEDEX 44613France

Offshore wind substations are subjected to uncertain loads from waves,wind and *** states are composed of irregular waves which statistics are usually *** loads may induce fatigue failure of some structural components of the *** combining fatigue damage computed through numerical simulations for each sea state endured by the structure,it is possible to assess fatigue failure of the structure over the whole deployment ***,the influence of the discretization error on the fatigue damage is rarely *** is possible to estimate the discretization error on the quantity of interest computed at the structural detail suspected to ***,the relation between this local quantity of interest and the fatigue damage is *** this paper,a method that allows propagating error bounds towards fatigue damage is *** increasing computational burden,computing discretization error bounds is a useful output of finite element *** can be utilized to either validate mesh choice or guide remeshing in case where potential error on the fatigue damage is too *** method is applied to an offshore wind substation developped by Chantiers de l’Atlantique using two discretization error estimators in a single sea state.

关键词： Offshore wind turbines Uncertainty propagation Fatigue damage discretization error