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Fazio Riccardo - One of the best experts on this subject based on the ideXlab platform.

  • The Non-Iterative Transformation Method
    2020
    Co-Authors: Fazio Riccardo
    Abstract:

    The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semi-infinite flat plate. The definition of a non-iterative transformation method for the celebrated Blasius Problem is due to T{\"o}pfer and dates more than a century ago. Here we define a non-iterative transformation method for Blasius equation with a moving wall, a slip flow condition or a surface gasification. The defined method allows us to deal with classes of Problems in boundary layer theory that, depending on a parameter, admit multiple or no solutions. This approach is particularly convenient when the main interest is on the behaviour of the considered models with respect to the involved parameter. The obtained numerical results are found to be in good agreement with those available in literature.Comment: 24 pages, 8 figures, 3 tables. arXiv admin note: substantial text overlap with arXiv:1501.0601

  • Numerical Transformation Methods for a Moving-Wall Boundary Layer Flow of a Rarefied Gas Free Stream over a Moving Flat Plate
    2020
    Co-Authors: Fazio Riccardo
    Abstract:

    The first contribution of this paper is the extension of the non-iterative transformation method, proposed by T\"opfer more than a century ago and defined for the numerical solution of the Blasius Problem, to a Blasius Problem with extended boundary conditions. This method, which makes use of the invariance of two physical parameters with respect to a scaling group of point transformation, allows us to solve numerically the Blasius Problem with extended boundary conditions by solving a related initial value Problem and then rescaling the obtained numerical solution. Therefore, our method is an initial value method. However, in this way, we cannot fix in advance the physical parameters, and if we need just to compute the numerical solution for given values of the two parameters we have to define an iterative extension of the transformation method, which is the second contribution of this work.Comment: 14 pages, 2 figures and 2 tables. arXiv admin note: substantial text overlap with arXiv:2003.0626

  • A Non-Iterative Transformation Method for an Extended Blasius Problem
    'Wiley', 2020
    Co-Authors: Fazio Riccardo
    Abstract:

    In this paper we define a non-iterative transformation method for an Extended Blasius Problem. The original non-iterative transformation method, which is based on scaling invariance properties, was defined for the classical Blasius Problem by T\"opfer in 1912. This method allows us to solve numerically a boundary value Problem by solving a related initial value Problem and then rescaling the obtained numerical solution. In recent years, we have seen applications of the non-iterative transformation method to several Problems of interest. The obtained numerical results, are improved by both a mesh refinement strategy and the Richardson's extrapolation technique.%, are found to be in good agreement with those available in literature.Comment: 12 pages,1 figure, 2 tables. arXiv admin note: substantial text overlap with arXiv:1501.0601

  • The Iterative Transformation Method
    2020
    Co-Authors: Fazio Riccardo
    Abstract:

    In a transformation method, the numerical solution of a given boundary value Problem is obtained by solving one or more related initial value Problems. Therefore, a transformation method, like a shooting method, is an initial value method. The main difference between a transformation and a shooting method is that the former is conceived and derive its formulation from the scaling invariance theory. This paper is concerned with the application of the iterative transformation method to several Problems in the boundary layer theory. The iterative method is an extension of the T{\"o}pfer's non-iterative algorithm developed as a simple way to solve the celebrated Blasius Problem. This iterative method provides a simple numerical test for the existence and uniqueness of solutions. Here we show how the method can be applied to Problems with a homogeneous boundary conditions at infinity and in particular we solve the Sakiadis Problem of boundary layer theory. Moreover, we show how to couple our method with Newton's root-finder. The obtained numerical results compare well with those available in the literature. The main aim here is that any method developed for the Blasius, or the Sakiadis, Problem might be extended to more challenging or interesting Problems. In this context, the iterative transformation method has been recently applied to compute the normal and reverse flow solutions of Stewartson for the Falkner-Skan model [Comput. \& Fluids, {\bf 73} (2013) pp. 202-209].Comment: 48 pages, 12 figures, 7 tables. arXiv admin note: substantial text overlap with arXiv:1212.5057, arXiv:1410.2043, arXiv:2003.0773

  • The Iterative Transformation Method for the Sakiadis Problem
    'Elsevier BV', 2014
    Co-Authors: Fazio Riccardo
    Abstract:

    In a transformation method the numerical solution of a given boundary value Problem is obtained by solving one or more related initial value Problems. This paper is concerned with the application of the iterative transformation method to the Sakiadis Problem. This method is an extension of the Toepfer's non-iterative algorithm developed as a simple way to solve the celebrated Blasius Problem. As shown by this author [Appl. Anal., 66 (1997) pp. 89-100] the method provides a simple numerical test for the existence and uniqueness of solutions. Here we show how the method can be applied to Problems with a homogeneous boundary conditions at infinity and in particular we solve the Sakiadis Problem of boundary layer theory. Moreover, we show how to couple our method with Newton's root-finder. The obtained numerical results compare well with those available in literature. The main aim here is that any method developed for the Blasius, or the Sakiadis, Problem might be extended to more challenging or interesting Problems. In this context, the iterative transformation method has been recently applied to compute the normal and reverse flow solutions of Stewartson for the Falkner-Skan model [Comput. & Fluids, 73 (2013) pp. 202-209].Comment: 19 pages, 3 figures, 3 table

Mehdi Dehghan - One of the best experts on this subject based on the ideXlab platform.

  • solution of a laminar boundary layer flow via a numerical method
    Communications in Nonlinear Science and Numerical Simulation, 2010
    Co-Authors: Kourosh Parand, M Shahini, Mehdi Dehghan
    Abstract:

    Abstract In this paper, the numerical solution of the Blasius Problem is obtained using the collocation method based on rational Chebyshev functions. The Blasius equation is a nonlinear ordinary differential equation which arises in the boundary layer flow. The method reduces solving the equation to solving a system of nonlinear algebraic equations. The results presented here demonstrate reliability and efficiency of the method.

Kourosh Parand - One of the best experts on this subject based on the ideXlab platform.

  • solution of a laminar boundary layer flow via a numerical method
    Communications in Nonlinear Science and Numerical Simulation, 2010
    Co-Authors: Kourosh Parand, M Shahini, Mehdi Dehghan
    Abstract:

    Abstract In this paper, the numerical solution of the Blasius Problem is obtained using the collocation method based on rational Chebyshev functions. The Blasius equation is a nonlinear ordinary differential equation which arises in the boundary layer flow. The method reduces solving the equation to solving a system of nonlinear algebraic equations. The results presented here demonstrate reliability and efficiency of the method.

Beong In Yun - One of the best experts on this subject based on the ideXlab platform.

G. I. Shishkin - One of the best experts on this subject based on the ideXlab platform.

  • c ○ 2000 MII ACCURATE NUMERICAL METHOD FOR Blasius ’ Problem FOR FLOW PAST A FLAT PLATE WITH MASS TRANSFER ∗
    2008
    Co-Authors: B. Gahan, J. J. H. Miller, G. I. Shishkin
    Abstract:

    We construct a new finite difference method for computing reference numerical solutions to the one–parameter family of Blasius ’ Problems arising from incompressible laminar flow past a thin flat plate with mass transfer by both suction and blowing. We show that, by studying several representative Problems in the family, the method generates nodal approximations, at a finite number of nodes, to the solution and its derivatives, the piecewise linear interpolants of which provide global pointwise accurate approximations to the solution and its derivatives on the semi–infinite domain [0, ∞). Using an experimental error estimate technique we determine orders of convergence and error constants of the reference numerical solutions and their discrete derivatives. Algebraic formulae for realistic pointwise error bounds, in terms of the number of mesh subintervals used in the discrete Problem, determine the number of mesh points required to achieve a given preassigned guaranteed accuracy in the reference numerical solutions of Blasius ’ Problem. Such reference numerical solutions to Blasius ’ Problem can be used to construct Re–uniformly accurate approximations to the components uP (x, y), vP (x, y) of the solution of Prandtl’s Problem and to their first order partial derivatives. 1

  • A Reynolds-uniform numerical method for Prandtl's boundary layer Problem for flow past a plate with mass transfer
    2007
    Co-Authors: J.s. Butler, J. J. H. Miller, G. I. Shishkin
    Abstract:

    In this paper we consider Prandtl's boundary layer Problem for incompressible laminar ow past a plate with transfer of uid through the surface of the plate. When the Reynolds number is large the solution of this Problem has a parabolic boundary layer. In a neighbourhood of the plate the solution of the Problem has an additional singularity which is caused by the absence of the compartability conditions. To solve this Problem outside nearest neighbourhood of the leading edge, we construct a direct numerical method for computing approximations to the solution of the Problem using a piecewise uniform mesh appropriately tted to the parabolic boundary layer. To validate this numerical method, the model Prandtl Problem with self-similar solution was examined, for which a reference solution can be computed using the Blasius Problem for a nonlinear ordinary dierential equation. For the model Problem, suction/blowing of the ow rate density is v 0 (x) = v i 2 , where the Reynolds number Re can be arbitrarily large and v i is the intensity of the mass transfer with arbitrary values in the segment [ :3; :3]. We considered the Prandtl Problem in a nite rectangle excluding the leading edge of the plate for various values of Re which can be arbitrary large and for some values of v i , when meshes with dierent number of mesh points were used. To nd reference solutions for the the velocity components and their derivatives with required accuracy, we solved the Blasius Problem using a semi{analytical numerical method. By extensive numerical experiments we showed that the direct numerical method constructed in this paper allows us to approximate both the solution and its derivatives Re{uniformly for dierent values of v i