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PROJECTION METHOD FOR VISCOUS INCOMPRESSIBLE-FLOW ON QUADRILATERAL GRIDS

AIAA JOURNAL 1994年第10期32卷 1961-1969页

作者： BELL, JB SZYMCZAK, WG USN CTR SURFACE WARFAREINFORMAT SCI & SYST BRANCHSILVER SPRINGMD 20903

This paper describes a second-order projection method for the incompressible Navier-Stokes equations on multiply connected domains with a logically rectangular quadrilateral grid. The method uses a second-order fractional step scheme in which one first solves diffusion-convection equations to determine intermediate velocities which are then projected onto the space of divergence-free vector fields. The spatial discretizations are accomplished by formally transforming the equations to a computational space with a uniform grid. The diffusion, pressure gradient, and divergence terms are discretized using standard finite difference approximations. The convection terms are discretized using a second-order Godunov method that provides a robust discretization of these terms at high Reynolds number. Numerical results are presented illustrating the performance of the method.

关键词： Incompressible Flow Reynolds Number Navier Stokes Equations Convection finite difference approximation Strouhal Numbers Computing Conjugate Gradient Algorithm Cartesian Coordinate System Riemann Problem

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Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control

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SIAM JOURNAL ON NUMERICAL ANALYSIS 1999年第3期36卷 667-695页

作者： Boué, M Dupuis, P Inst Tecnol Autonomo Mexico Dept Matemat Mexico City 01000 DF Mexico Brown Univ Div Appl Math Lefschetz Ctr Dynam Syst Providence RI 02912 USA

We consider the construction of Markov chain approximations for an important class of deterministic control problems. The emphasis is on the construction of schemes that can be easily implemented and which possess a number of highly desirable qualitative properties. The class of problems covered is that for which the control is affine in the dynamics and with quadratic running cost. This class covers a number of interesting areas of application, including problems that arise in large deviations, risk-sensitive and robust control, robust filtering, and certain problems in computer vision. Examples are given as well as a proof of convergence.

关键词： Markov chain approximation finite difference approximation deterministic optimal control weak convergence calculus of variations

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DETERMINATION OF AERODYNAMIC SENSITIVITY COEFFICIENTS BASED ON THE TRANSONIC SMALL PERTURBATION FORMULATION

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JOURNAL OF AIRCRAFT 1990年第6期27卷 507-515页

作者： ELBANNA, HM CARLSON, LA Texas A&M University College Station Texas 77843

The quasianalytical approach is developed to compute airfoil aerodynamic sensitivity coefficients in the transonic and supersonic flight regimes. Initial investigation verifies the feasibility of this approach as applied to the transonic small perturbation residual expression. Results are compared to those obtained by the direct (finite difference) approach, and both methods are evaluated to determine their computational accuracies and efficiencies. The quasianalytical approach is shown to yield more accurate coefficients and is potentially more efficient and worth further investigation. © 1989 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

关键词： Lift Coefficient Freestream Mach Number Airfoil Geometry Computing Pressure Coefficient Thin Airfoil Theory Supersonic Flight Computational Fluid Dynamics finite difference approximation Gaussian Elimination

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SM-Algorithms for Approximating the Variable-Order Fractional Derivative of High Order

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FUNDAMENTA INFORMATICAE 2017年第1-4期151卷 293-311页

作者： Moghaddam, B. P. Machado, J. A. T. Islamic Azad Univ Lahijan Branch Dept Math Lahijan Iran Inst Engn Dept Elect Engn Rua Dr Antonio Bernardino Almeida 431 P-4249015 Oporto Portugal

In this paper we discuss different definitions of variable-order derivatives of high order and we propose accurate and robust algorithms for their approximate calculation. The proposed algorithms are based on finite difference approximations and B-spline interpolation. We compare the performance of the algorithms by experimental convergence order. Numerical examples are presented demonstrating the efficiency and accuracy of the proposed algorithms.

关键词： Fractional calculus Variable-order derivative Spline approximation finite difference approximation Convergence order Numerical method

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EFFECT OF SURFACE DEFORMATION ON THERMOCAPILLARY BUBBLE MIGRATION

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AIAA JOURNAL 1992年第4期30卷 993-998页

作者： CHEN, JC LEE, YT National Central University Chung-Li Taiwan 32054 Republic of China

Under microgravity environments, the thermocapillary migration of a deformable gas bubble placed in a liquid with a constant temperature gradient is investigated numerically. A finite difference method with boundary-fitted coordinates is employed to solve the axisymmetric governing equations. An iterative procedure is introduced for the computation of the deformable shape and the thermal velocity of the gas bubble. The influence of the Marangoni and capillary number is considered. Results of the computations show that the terminal velocity of the gas bubble is reduced significantly by the effect of surface deformation.

关键词： Terminal Velocity Capillary Numbers finite difference approximation Microgravity Kinematic Viscosity Normal Stress Temperature Fields Prandtl Number Heat Transfer Coefficients Shape Functions

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INVERSE DETERMINATION OF THERMAL-CONDUCTIVITY FOR ONE-DIMENSIONAL PROBLEMS

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1995年第2期9卷 335-344页

作者： LAM, TT YEUNG, WK AEROSP CORP DIV VEHICLE SYST OPTIMIZAT TECH SECT EL SEGUNDO CA 90245 USA

Two finite difference procedures are presented for the inverse determination of the thermal conductivity in a one-dimensional heal conduction domain. The thermal conductivity is reconstructed from the inverse analysis based on the assumption that the temperature measurements are either available continuously over the entire domain or at discrete grid points. The convergence and stability of the computational algorithms are investigated, It is concluded that both procedures are first-order accurate methods. A comparison of the exact thermal conductivity with the one estimated was made to confirm the validity of the numerical procedures. The close agreement between the two results confirms that the proposed finite difference techniques are effective procedures for the inverse determination of thermal conductivity in a one-dimensional heat conduction domain. The methods are applicable for linear and nonlinear spatially- as well as temperature-dependent thermal conductivities. Additionally, the special feature of the present techniques is that a priori knowledge of the functional form for the thermal conductivity is not mandatory.

关键词： Thermal Conductivity Inverse Heat Conduction Backward Euler Method Conduction Equation Heat Generation Thermal Management System finite difference approximation Heat Transfer Convection finite Element Formulation

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A numerical method for a nonlinear structured population model with an indefinite growth rate coupled with the environment

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NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2019年第6期35卷 2348-2374页

作者： Ackleh, Azmy S. Miller, Robert L. Univ Louisiana Lafayette Dept Math Lafayette LA 70504 USA Univ Louisiana Lafayette Dept Civil Engn Lafayette LA 70504 USA

A numerical method is developed for a general structured population model coupled with the environment dynamics over a bounded domain where the individual growth rate changes sign. Sign changes notably exhibit nonlocal dependence on the population density and environmental factors (e.g., resource availability and other habitat variables). This leads to a highly nonlinear PDE describing the time-evolution of the population density coupled with a nonlinear-nonlocal system of ODEs describing the environmental time-dynamics. Stability of the finite-difference numerical scheme and its convergence to the unique weak solution are proved. Numerical experiments are provided to demonstrate the performance of the finite difference scheme and to illustrate a range of biologically relevant potential applications.

关键词： convergence environment finite difference approximation indefinite growth rates structured population models

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Modeling erythropoiesis subject to malaria infection

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MATHEMATICAL BIOSCIENCES 2010年第1期225卷 59-67页

作者： Thibodeaux, Jeremy J. Univ Cent Oklahoma Dept Math & Stat Edmond OK 73034 USA

A mathematical model of erythropoiesis subject to malaria infection is developed by combining ideas from previous models that addressed only one of the two phenomena. The nature of the model allows one to account for suppression of erythropoiesis by the toxin hemozoin, which is a by-product of digested hemoglobin. Following the derivation of the model, numerical simulations are performed and show that the number of parasites produced per bursting erythrocyte has the most significant effect of erythropoiesis. It is also shown that removing hemozoin may be an effective method for aiding the recovery of the erythrocyte population, but is not effective in maintaining a healthy population in the early stages of infection. The second half of the paper introduces an implicit finite difference scheme that was used to perform the simulations previously mentioned. An existence-uniqueness result is then provided via the numerical method. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Structured model Erythropoiesis Malaria finite difference approximation Existence-uniqueness Numerical simulations

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NUMERICAL-SIMULATION OF RAREFIED-GAS FLOW THROUGH A SLIT

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1992年第1期6卷 27-34页

作者： CHUNG, CH JENG, DR DEWITT, KJ KEITH, TG UNIV TOLEDO DEPT CHEM ENGN TOLEDO OH 43606 USA UNIV TOLEDO DEPT MECH ENGN TOLEDO OH 43606 USA

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte-Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for a vacuum downstream, finite pressure ratios, and isobaric conditions with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations that are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere (VHS) model is used as a molecular model and the no time counter (NTC) method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by a factor of 4 in CPU memory size and by factors of 10 to 40 in CPU time, depending on the degree of gas rarefaction.

关键词： Bhatnagar Gross Krook Direct Simulation Monte Carlo finite difference approximation Boltzmann Equation Thermal Diffusion Knudsen Numbers Free Molecular Flow Viscosity Mass Flow Rate Cartesian Coordinate System

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NONEQUILIBRIUM HYPERSONIC FLOWS OVER CORNERS

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AIAA JOURNAL 1991年第2期29卷 235-241页

作者： PANDOLFI, M ARINA, R BOTTA, N Politecnico di Torino Torino Italy

The hypersonic nonequilibrium flow of air over concave and convex corners is investigated. The description of the flowfield is based on the Euler equations and a chemical model that accounts for the finite rate reactions. An upwind formulation and the related space-marching technique are developed in order to achieve the numerical solution of the fluid dynamical and chemical equations, coupled together. The attention is focused on the effects of nonequilibrium chemistry on fluid dynamics. The transition from the frozen flow condition, just behind the corner, and the equilibrium flow, reached at very large distances far downstream, is characterized by intermediate strong nonequilibrium chemical processes. Such a transition promotes dissipations that, in turn, generate vorticity.

关键词： Nonequilibrium Flows Damköhler Numbers Equations of Fluid Dynamics Shock Layers Prandtl Meyer Expansion Fan Oblique Shock Convection Compressibility finite difference approximation Thermal Conductivity

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