In quasi-steady-state creeping flow it is possible to combine the mass conservation equation and the momentum equation to generate a new equation in terms of the stream function W: (V*Y = 0). Here, V is called the biharmonic operator. In cartesian coordinate, this operator is defined a4 a2 a4 V4= +2 Derive a second order central difference discretization of the biharmonic equation.

In quasi-steady-state creeping flow it is possible to combine the mass conservation equation and the momentum equation to generate a new equation in terms of the stream function W: (V*Y = 0). Here, V is called the biharmonic operator. In cartesian coordinate, this operator is defined a4 a2 a4 V4= +2 Derive a second order central difference discretization of the biharmonic equation.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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