http://inis.jinr.ru/sl/m_mathematics/mn_numerical methods/mnd_numerical calculus/allgower e.l., georg k. introduction to numerical continuation methods (colorado, 1990)(397s).pdf

Numerical Continuation Methods

This article reviews acoustic microfiuidics: the use of acoustic fields, principally ultrasonics, for application in microfiuidics. Although acoustics is a classical field, its promising, and indeed perplexing, capabilities in powerfully manipulating both fluids and particles within those fluids on the microscale to nanoscale has revived interest in it. The bewildering state of the literature and ample jargon from decades of research is reorganized and presented in the context of models derived from first principles. This hopefully will make the area accessible for researchers with experience in materials science, fluid mechanics, or dynamics. The abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques common in microfluidics, along with the many applications in microfluidics and nanofluidics that appear through the literature.

/pdf/microscale-acoustofluidics-microfluidics-driven-via-5bet39j13p.pdf

Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics

https://www.southampton.ac.uk/~nwb/lectures/GoodPracticeCFD/Articles/Validation_SAND2002-0529.pdf

Verification and Validation in Computational Fluid Dynamics

From the Publisher:
Introduction to Numerical Continuation Methods continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business looking for an introduction to computational methods for solving a large variety of nonlinear systems of equations. A background in elementary analysis and linear algebra is adequate preparation for reading this book; some knowledge from a first course in numerical analysis may also be helpful.

/pdf/introduction-to-numerical-continuation-methods-ily9kpadk5.pdf

Introduction to Numerical Continuation Methods

Recent advances in nonlinear passive vibration isolators

The stagnation flow towards a shrinking sheet is studied. A similarity transform reduces the Navier–Stokes equations to a set of non-linear ordinary differential equations which are then integrated numerically. Both two-dimensional and axisymmetric stagnation flows are considered. It is found that solutions do not exist for larger shrinking rates and may be non-unique in the two-dimensional case. The non-alignment of the stagnation flow and the shrinking sheet complicates the flow structure. Convective heat transfer decreases with the shrinking rate due to an increase in boundary layer thickness.

Stagnation flow towards a shrinking sheet

The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.

/pdf/viscous-flow-due-to-a-shrinking-sheet-1l64h5m1fq.pdf

Viscous flow due to a shrinking sheet

1. The solutions represent fundamental fluid-dynamic flows. Also, owing to the uniform validity of exact solutions, the basic phenomena described by the Navier-Stokes equations can be more closely studied. 2. The exact solutions serve as standards for checking the accuracies of the many approximate methods, whether they are numerical, asymp­ totic, or empirical. Current advances in computer technology make the complete numerical integration of the Navier-Stokes equations more feasible. However, the accuracy of the results can only be ascertained by a comparison with an exact solution.

Exact Solutions of the Steady-State Navier-Stokes Equations

The unsteady Navier-Stokes equations are a set of nonlinear partial differential equations with very few exact solutions. This paper attempts to classify and review the existing unsteady exact solutions. There are three main categories: parallel, concentric and related solutions, Beltrami and related solutions, and similarity solutions. Physically significant examples are emphasized.

Exact Solutions of the Unsteady Navier-Stokes Equations

The complete post-buckling and large deformations of an elastica rod, one end fixed and one end pinned, is studied through perturbations near bifurcation, asymptotic analysis for large loads and a numerical integration scheme. The bifurcation curve is not monotonic. The post-buckling behavior exhibits non-linear phenomena such as limit load, non-uniqueness, hysteresis, and violent jumps.

C.Y. Wang

Papers

Stagnation flow towards a shrinking sheet

Viscous flow due to a shrinking sheet

Exact Solutions of the Steady-State Navier-Stokes Equations

Exact Solutions of the Unsteady Navier-Stokes Equations

Post-buckling of a clamped-simply supported elastica