School of Mathematics and Statistics

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Browsing School of Mathematics and Statistics by Author "Amaranath, T."
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    A complete general solution of the unsteady Brinkman equations
    ( 2018-05-15) Tumuluri, Suman Kumar ; Amaranath, T.
    In this paper, we present a complete general solution of the unsteady Brinkman equations. To this end, we introduce a representation for velocity and pressure in terms of two scalar functions. One of these scalar functions satisfies a second order partial differential equation (PDE) while the other satisfies a fourth order PDE which can be factorized into a pair of second order PDEs. We show that the solution of this fourth order PDE is indeed the sum of the solutions of the two second order PDEs. We also use these solutions to obtain a complete general solution of the unsteady Brinkman equations.
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    A factorization theorem for operators occurring in the Stokes, Brinkman and Oseen equations
    ( 2016-03-05) Tumuluri, Suman Kumar ; Amaranath, T.
    In many physical problems one is faced with solving partial differential equations of the form L1(L1+L2)u=0, where L1 and L2 are linear operators. It is found in many cases that the solution u is of the form u1+u2 where L1u1=0 and (L1+L2)u2=0. In this paper we present sufficient conditions under which such a splitting is possible. Moreover, we give explicit formulae for u1 and u2 for a given u. We also show in some examples where the operators satisfy the sufficient conditions and such a splitting is used extensively. In particular, we find a class of solutions for the unsteady Brinkman and unsteady Oseen equations using the splitting that we propose.
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    A new approximate analytical solution for arbitrary Stokes flow past rigid bodies
    ( 2012-12-01) Radha, R. ; Sri Padmavati, B. ; Amaranath, T.
    A method of computing general Stokes flows in the presence of rigid boundaries of arbitrary shape is proposed. The solution satisfies the governing field equations exactly and the boundary conditions approximately. The method has been illustrated with three examples. The advantage of the method lies in the ease of implementation for rigid bodies of arbitrary shape, providing an approximate but analytical solution throughout the domain. © 2012 Springer Basel AG.
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    New approximate analytical solutions for creeping flow past axisymmetric rigid bodies
    ( 2010-03-01) Radha, R. ; Padmavathi, B. S. ; Amaranath, T.
    We describe a new approximate method to discuss uniform flow past rigid bodies of two different shapes using a complete general solution (Palaniappan et al., 1992; Padmavathi et al., 1998) of Stokes equations in an incompressible, viscous fluid. We also sketch the streamlines in both the cases. However, the solution, although approximate, has an added advantage that it is known at all the points in the domain since it is given in an analytical form, unlike the numerical methods like finite difference methods or finite element methods which use meshes, where the solution is known only at certain predetermined points. This method hence enables us to obtain in a simple way, more accurate values of physical quantities like the drag experienced by a rigid body, even though the solution may be approximate. We also note that the method can easily be extended to other arbitrary axisymmetric Stokes flows also. © 2009 Elsevier Ltd. All rights reserved.