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Efficient Numerical Method (efficient + numerical_method)
Selected AbstractsA linearized implicit pseudo-spectral method for some model equations: the regularized long wave equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2003K. Djidjeli Abstract An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. =10pt An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations (Equation (2)), with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source] Volume determination for bulk materials in bunkersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2004S. A. Ahmed Abstract A simple model for the determination of the shape of large granular piles in complicated geometries is discussed. An eikonal formulation of the problem is proposed. Two distinct cases arise. In cylindrical geometries, i.e., if both container and possible obstacles have vertical walls, the problem is equivalent to a two-dimensional travel time problem with obstacles, while in general geometries, this analogy breaks down. In the first case, classical one-sided discretizations are generalized to handle obstacles without loss in accuracy. In the second case, a fast and efficient numerical method is proposed, implemented and tested. The discrete problems are solved through fast marching. Copyright © 2004 John Wiley & Sons, Ltd. [source] Semi-discretization method for delayed systemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2002Tamás Insperger Abstract The paper presents an efficient numerical method for the stability analysis of linear delayed systems. The method is based on a special kind of discretization technique with respect to the past effect only. The resulting approximate system is delayed and also time periodic, but still, it can be transformed analytically into a high-dimensional linear discrete system. The method is applied to determine the stability charts of the Mathieu equation with continuous time delay. Copyright © 2002 John Wiley & Sons, Ltd. [source] Semi-Lagrangian advection on a spherical geodesic gridINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2007Maria Francesca Carfora Abstract A simple and efficient numerical method for solving the advection equation on the spherical surface is presented. To overcome the well-known ,pole problem' related to the polar singularity of spherical coordinates, the space discretization is performed on a geodesic grid derived by a uniform triangulation of the sphere; the time discretization uses a semi-Lagrangian approach. These two choices, efficiently combined in a substepping procedure, allow us to easily determine the departure points of the characteristic lines, avoiding any computationally expensive tree-search. Moreover, suitable interpolation procedures on such geodesic grid are presented and compared. The performance of the method in terms of accuracy and efficiency is assessed on two standard test cases: solid-body rotation and a deformation flow. Copyright © 2007 John Wiley & Sons, Ltd. [source] Fourth-order compact formulation of Navier,Stokes equations and driven cavity flow at high Reynolds numbersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006E. Erturk Abstract A new fourth-order compact formulation for the steady 2-D incompressible Navier,Stokes equations is presented. The formulation is in the same form of the Navier,Stokes equations such that any numerical method that solve the Navier,Stokes equations can easily be applied to this fourth-order compact formulation. In particular, in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601 × 601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number with Re = 20 000 fourth-order spatial accuracy. Detailed solutions are presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] Simulation of two-dimensional turbulent flows in a rotating annulusINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2004Brian D. Storey Abstract Rotating water tank experiments have been used to study fundamental processes of atmospheric and geophysical turbulence in a controlled laboratory setting. When these tanks are undergoing strong rotation the forced turbulent flow becomes highly two dimensional along the axis of rotation. An efficient numerical method has been developed for simulating the forced quasi-geostrophic equations in an annular geometry to model current laboratory experiments. The algorithm employs a spectral method with Fourier series and Chebyshev polynomials as basis functions. The algorithm has been implemented on a parallel architecture to allow modelling of a wide range of spatial scales over long integration times. This paper describes the derivation of the model equations, numerical method, testing and performance of the algorithm. Results provide reasonable agreement with the experimental data, indicating that such computations can be used as a predictive tool to design future experiments. Copyright © 2004 John Wiley & Sons, Ltd. [source] An implicit velocity decoupling procedure for the incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2002Kyoungyoun Kim Abstract An efficient numerical method to solve the unsteady incompressible Navier,Stokes equations is developed. A fully implicit time advancement is employed to avoid the Courant,Friedrichs,Lewy restriction, where the Crank,Nicolson discretization is used for both the diffusion and convection terms. Based on a block LU decomposition, velocity,pressure decoupling is achieved in conjunction with the approximate factorization. The main emphasis is placed on the additional decoupling of the intermediate velocity components with only nth time step velocity. The temporal second-order accuracy is preserved with the approximate factorization without any modification of boundary conditions. Since the decoupled momentum equations are solved without iteration, the computational time is reduced significantly. The present decoupling method is validated by solving several test cases, in particular, the turbulent minimal channel flow unit. Copyright © 2002 John Wiley & Sons, Ltd. [source] The reduced scalar potential in regions with permeable materials: Reasons for loss of accuracy and cancellationINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 4 2007S. Balac Abstract Practical three-dimensional magnetic field problems usually involve regions containing current sources as well as regions with magnetic materials. For computational purposes, the use of the reduced scalar potential (RSP) as unknown has the advantage to transform a problem for a vector field throughout the space into a problem for a scalar function, thus reducing the number of degrees of freedom in the discretization. However, in regions with high magnetic permeability the use of the RSP alone usually results in severe loss in accuracy and it is recommended to use both the RSP and the total scalar potential. Using an asymptotic expansion, we investigate theoretically the underlying reasons for this lack of accuracy in permeable regions when using the RSP as a unique potential. Moreover, this investigation leads to an efficient numerical method to compute the magnetic field in regions with high magnetic permeability. Copyright © 2007 John Wiley & Sons, Ltd. [source] | ||||||||||