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Dynamics Problems (dynamics + problem)

Distribution by Scientific Domains
Engineering84%

Kinds of Dynamics Problems

  • fluid dynamics problem
    		•

    Selected Abstracts

    A preconditioner freeze strategy for numerical solution of compressible flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2003
    R. S. Silva
    Abstract It is well known that Krylov,Schwarz methods are well suited for solving linear systems of equations in high-latency, distributed memory environments and constitute powerful tools when combined with Newton,Krylov methods to solve Computational Fluid Dynamics problems. Nevertheless, the computational costs related to the Jacobian and the preconditioner evaluation can sometimes be prohibitive. In this work a strategy to reduce these costs is presented, based on evaluating a new preconditioner only after it had been frozen for several time steps. Numerical experiments show the computational gain achieved with the proposed strategy. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Optimal flow control for Navier,Stokes equations: drag minimization

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007
    L. Dedè
    Abstract Optimal control and shape optimization techniques have an increasing role in Fluid Dynamics problems governed by partial differential equations (PDEs). In this paper, we consider the problem of drag minimization for a body in relative motion in a fluid by controlling the velocity through the body boundary. With this aim, we handle with an optimal control approach applied to the steady incompressible Navier,Stokes equations. We use the Lagrangian functional approach and we consider the Lagrangian multiplier method for the treatment of the Dirichlet boundary conditions, which include the control function itself. Moreover, we express the drag coefficient, which is the functional to be minimized, through the variational form of the Navier,Stokes equations. In this way, we can derive, in a straightforward manner, the adjoint and sensitivity equations associated with the optimal control problem, even in the presence of Dirichlet control functions. The problem is solved numerically by an iterative optimization procedure applied to state and adjoint PDEs which we approximate by the finite element method. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    An improved study of real-time fluid simulation on GPU

    COMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3-4 2004
    Enhua Wu
    Abstract Taking advantage of the parallelism and programmability of GPU, we solve the fluid dynamics problem completely on GPU. Different from previous methods, the whole computation is accelerated in our method by packing the scalar and vector variables into four channels of texels. In order to be adaptive to the arbitrary boundary conditions, we group the grid nodes into different types according to their positions relative to obstacles and search the node that determines the value of the current node. Then we compute the texture coordinates offsets according to the type of the boundary condition of each node to determine the corresponding variables and achieve the interaction of flows with obstacles set freely by users. The test results prove the efficiency of our method and exhibit the potential of GPU for general-purpose computations. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Implicit J2 -bounding surface plasticity using Prager's translation rule

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2002
    Francisco J. Montáns
    Abstract A bounding surface J2 -plasticity model that uses Prager's translation rule is presented. The model preserves Masing's rules and is developed from the same ideas as classical infinitesimal J2 -plasticity, resulting in the same formulation with the exception of the algorithm for the computation of the hardening function. Instead of utilizing a loading surface as in a previous formulation, hardening surfaces are introduced; the formulation is similar to that of multilayer plasticity using Prager's rule, presented in previous work. An implicit algorithm based on the radial return concept is used, and the consistent elastoplastic tangent is also developed in closed form. Examples illustrating anisotropic behaviour are presented and compared to that predicted by a multilayer J2 -plasticity model. The model is also applied to a soil dynamics problem to show the robustness of the algorithm and its applicability to complex loading. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Multi-time-step domain coupling method with energy control

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010
    N. Mahjoubi
    Abstract A multi-time-step integration method is proposed for solving structural dynamics problems on multiple domains. The method generalizes earlier state-space integration algorithms by introducing displacement constraints via Lagrange multipliers, representing the time-integrated constraint forces over the individual time step. It is demonstrated that displacement continuity between the subdomains leads to cancelation of the interface contributions to the energy balance equation, and thus stability and algorithmic damping properties of the original algorithms are retained. The various subdomains can be integrated in time using different time steps and/or different state-space time integration schemes. The solution of the constrained system equations is obtained using a dual Schur formulation, allowing for maximum independence of the calculation of the subdomains. Stability and accuracy are illustrated by a numerical example using a refined mesh around concentrated forces. Copyright © 2010 John Wiley & Sons, Ltd. [source]

    A time-parallel implicit method for accelerating the solution of non-linear structural dynamics problems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009
    Julien Cortial
    Abstract The parallel implicit time-integration algorithm (PITA) is among a very limited number of time-integrators that have been successfully applied to the time-parallel solution of linear second-order hyperbolic problems such as those encountered in structural dynamics. Time-parallelism can be of paramount importance to fast computations, for example, when space-parallelism is unfeasible as in problems with a relatively small number of degrees of freedom in general, and reduced-order model applications in particular, or when reaching the fastest possible CPU time is desired and requires the exploitation of both space- and time-parallelisms. This paper extends the previously developed PITA to the non-linear case. It also demonstrates its application to the reduction of the time-to-solution on a Linux cluster of sample non-linear structural dynamics problems. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2004
    X. Zhou
    Abstract The primary objectives of the present exposition are to: (i) provide a generalized unified mathematical framework and setting leading to the unique design of computational algorithms for structural dynamic problems encompassing the broad scope of linear multi-step (LMS) methods and within the limitation of the Dahlquist barrier theorem (Reference [3], G. Dahlquist, BIT 1963; 3: 27), and also leading to new designs of numerically dissipative methods with optimal algorithmic attributes that cannot be obtained employing existing frameworks in the literature, (ii) provide a meaningful characterization of various numerical dissipative/non-dissipative time integration algorithms both new and existing in the literature based on the overshoot behavior of algorithms leading to the notion of algorithms by design, (iii) provide design guidelines on selection of algorithms for structural dynamic analysis within the scope of LMS methods. For structural dynamics problems, first the so-called linear multi-step methods (LMS) are proven to be spectrally identical to a newly developed family of generalized single step single solve (GSSSS) algorithms. The design, synthesis and analysis of the unified framework of computational algorithms based on the overshooting behavior, and additional algorithmic properties such as second-order accuracy, and unconditional stability with numerical dissipative features yields three sub-classes of practical computational algorithms: (i) zero-order displacement and velocity overshoot (U0-V0) algorithms; (ii) zero-order displacement and first-order velocity overshoot (U0-V1) algorithms; and (iii) first-order displacement and zero-order velocity overshoot (U1-V0) algorithms (the remainder involving high-orders of overshooting behavior are not considered to be competitive from practical considerations). Within each sub-class of algorithms, further distinction is made between the design leading to optimal numerical dissipative and dispersive algorithms, the continuous acceleration algorithms and the discontinuous acceleration algorithms that are subsets, and correspond to the designed placement of the spurious root at the low-frequency limit or the high-frequency limit, respectively. The conclusion and design guidelines demonstrating that the U0-V1 algorithms are only suitable for given initial velocity problems, the U1-V0 algorithms are only suitable for given initial displacement problems, and the U0-V0 algorithms are ideal for either or both cases of given initial displacement and initial velocity problems are finally drawn. For the first time, the design leading to optimal algorithms in the context of a generalized single step single solve framework and within the limitation of the Dahlquist barrier that maintains second-order accuracy and unconditional stability with/without numerically dissipative features is described for structural dynamics computations; thereby, providing closure to the class of LMS methods. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    A-scalability and an integrated computational technology and framework for non-linear structural dynamics.

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003
    Part 1: Theoretical developments, parallel formulations
    Abstract For large-scale problems and large processor counts, the accuracy and efficiency with reduced solution times and attaining optimal parallel scalability of the entire transient duration of the simulation for general non-linear structural dynamics problems poses many computational challenges. For transient analysis, explicit time operators readily inherit algorithmic scalability and consequently enable parallel scalability. However, the key issues concerning parallel simulations via implicit time operators within the framework and encompassing the class of linear multistep methods include the totality of the following considerations to foster the proposed notion of A-scalability: (a) selection of robust scalable optimal time discretized operators that foster stabilized non-linear dynamic implicit computations both in terms of convergence and the number of non-linear iterations for completion of large-scale analysis of the highly non-linear dynamic responses, (b) selecting an appropriate scalable spatial domain decomposition method for solving the resulting linearized system of equations during the implicit phase of the non-linear computations, (c) scalable implementation models and solver technology for the interface and coarse problems for attaining parallel scalability of the computations, and (d) scalable parallel graph partitioning techniques. These latter issues related to parallel implicit formulations are of interest and focus in this paper. The former involving parallel explicit formulations are also a natural subset of the present framework and have been addressed previously in Reference 1 (Advances in Engineering Software 2000; 31: 639,647). In the present context, of the key issues, although a particular aspect or a solver as related to the spatial domain decomposition may be designed to be numerically scalable, the totality of the aforementioned issues simultaneously play an important and integral role to attain A-scalability of the parallel formulations for the entire transient duration of the simulation and is desirable for transient problems. As such, the theoretical developments of the parallel formulations are first detailed in Part 1 of this paper, and the subsequent practical applications and performance results of general non-linear structural dynamics problems are described in Part 2 of this paper to foster the proposed notion of A-scalability. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    A gradient smoothing method (GSM) for fluid dynamics problems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2008
    G. R. Liu
    Abstract A novel gradient smoothing method (GSM) based on irregular cells and strong form of governing equations is presented for fluid dynamics problems with arbitrary geometries. Upon the analyses about the compactness and the positivity of coefficients of influence of their stencils for approximating a derivative, four favorable schemes (II, VI, VII and VIII) with second-order accuracy are selected among the total eight proposed discretization schemes. These four schemes are successively verified and carefully examined in solving Poisson's equations, subjected to changes in the number of nodes, the shapes of cells and the irregularity of triangular cells, respectively. Numerical results imply us that all the four schemes give very good results: Schemes VI and VIII produce a slightly better accuracy than the other two schemes on irregular cells, but at a higher cost in computation. Schemes VII and VIII that consistently rely on gradient smoothing operations are more accurate than Schemes II and VI in which directional correction is imposed. It is interestingly found that GSM is insensitive to the irregularity of meshes, indicating the robustness of the presented GSM. Among the four schemes of GSM, Scheme VII outperforms the other three schemes, for its outstanding overall performance in terms of numerical accuracy, stability and efficiency. Finally, GSM solutions with Scheme VII to some benchmarked compressible flows including inviscid flow over NACA0012 airfoil, laminar flow over flat plate and turbulent flow over an RAE2822 airfoil are presented, respectively. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    A particle finite element method applied to long wave run-up

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2006
    J. Birknes
    Abstract This paper presents a Lagrangian,Eulerian finite element formulation for solving fluid dynamics problems with moving boundaries and employs the method to long wave run-up. The method is based on a set of Lagrangian particles which serve as moving nodes for the finite element mesh. Nodes at the moving shoreline are identified by the alpha shape concept which utilizes the distance from neighbouring nodes in different directions. An efficient triangulation technique is then used for the mesh generation at each time step. In order to validate the numerical method the code has been compared with analytical solutions and a preexisting finite difference model. The main focus of our investigation is to assess the numerical method through simulations of three-dimensional dam break and long wave run-up on curved beaches. Particularly the method is put to test for cases where different shoreline segments connect and produce a computational domain surrounding dry regions. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    On the use of the super compact scheme for spatial differencing in numerical models of the atmosphere

    THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 609 2005
    V. Esfahanian
    Abstract The ,Super Compact Finite-Difference Method' (SCFDM) is applied to spatial differencing of some prototype linear and nonlinear geophysical fluid dynamics problems. An alternative form of the SCFDM relations for spatial derivatives is derived. The sixth-order SCFDM is compared in detail with the conventional fourth-order compact and the second-order centred differencing. For the frequency of linear inertia-gravity waves on different numerical grids (Arakawa's A,E and Randall's Z) related to the Rossby adjustment process, the sixth-order SCFDM shows a substantial improvement on the conventional methods. For the Jacobians involved in vorticity advection by non-divergent flow and in the Bolin,Charney balance equation, a general framework, valid for every finite-difference method, is derived to present the discrete forms of the Jacobians. It is found that the sixth-order SCFDM provides a noticeably more accurate representation of the wave-number distribution of the Jacobians, when compared with the conventional methods. The problem of reconstructing the stream-function field from the vorticity field on a sphere is also considered. For the Rossby,Haurwitz wave, the computation of a normalized global error at different horizontal resolutions in longitude and latitude directions shows that the sixth-order SCFDM can markedly improve on the fourth-order compact. The sixth-order SCFDM is thus proposed as a viable method to improve the accuracy of finite-difference models of the atmosphere. Copyright © 2005 Royal Meteorological Society. [source]