Inclined wall plumes in porous media

Pop, I.

doi:10.1016/s0169-5983(97)81115-x

“…The matrix A (i) is called a block arrow-like matrix here due to its shape. A suitable algorithm for solving the matrix equation in (10) is the direct factorization method of block arrow-like matrix [6][7][8][9][10][11][12]. Algorithmically this is simply a modification of the usual solution of a block tridiagonal system to include the block arrow-like matrix and can be made efficient by taking account of the zeros appearing in matrices, comparing with the classical methods [13][14][15][16].…”

Section: Solution Of the Difference Equationsmentioning

confidence: 99%

An Accurate Numerical Method for Systems of Differentio-Integral Equations

Shu

¹

2013

Lecture Notes in Computer Science

0

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Abstract.A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method, it solves the problem of systems of differential equations involving integral operators not previously considered by the Keller Box method. Two main preparatory stages are required: (i) a merging procedure for differential equations and conditions without integral operators and; (ii) a reduction procedure for differential equations and conditions with integral operators. The differencing processes are effectively simplified by means of the unit-step function. The nonlinear difference equations are solved by Newton's method using an efficient block arrow-like matrix factorization technique. As an example of the application of this method, the systems of equations for combined gravity body force and forced convection in laminar film condensation can be solved for prescribed values of physical constants.

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“…The matrix A (i) is called a block arrow-like matrix here due to its shape. A suitable algorithm for solving the matrix equation in (10) is the direct factorization method of block arrow-like matrix [6][7][8][9][10][11][12]. Algorithmically this is simply a modification of the usual solution of a block tridiagonal system to include the block arrow-like matrix and can be made efficient by taking account of the zeros appearing in matrices, comparing with the classical methods [13][14][15][16].…”

Section: Solution Of the Difference Equationsmentioning

confidence: 99%

An accurate numerical method for systems of differentio-integral equations associated with multiphase flow

Sun¹

1996

International Journal of Multiphase Flow

0

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Abstract.A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method, it solves the problem of systems of differential equations involving integral operators not previously considered by the Keller Box method. Two main preparatory stages are required: (i) a merging procedure for differential equations and conditions without integral operators and; (ii) a reduction procedure for differential equations and conditions with integral operators. The differencing processes are effectively simplified by means of the unit-step function. The nonlinear difference equations are solved by Newton's method using an efficient block arrow-like matrix factorization technique. As an example of the application of this method, the systems of equations for combined gravity body force and forced convection in laminar film condensation can be solved for prescribed values of physical constants.

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“…In the field of viscous fluids there are many papers dealing with aspect of group theory transformation [(1952, 1968, 1999, 2006, 2009, 2011, 2012) ]. Shu and Pop (1997) numerically studied the natural convection from inclined wall plumes in a porous medium. The velocity is increased while the temperature is decreased with increasing the tilting angle.…”

Section: Introductionmentioning

confidence: 99%