Download e-book for iPad: High-order methods for incompressible fluid flow by Deville M.O., Fischer P.F., Mund E.H.

By Deville M.O., Fischer P.F., Mund E.H.

ISBN-10: 0521453097

ISBN-13: 9780521453097

High-order numerical tools supply a good method of simulating many actual difficulties. This ebook considers the variety of mathematical, engineering, and machine technological know-how subject matters that shape the root of high-order numerical equipment for the simulation of incompressible fluid flows in advanced domain names. Introductory chapters current high-order spatial and temporal discretizations for one-dimensional difficulties. those are prolonged to a number of area dimensions with an in depth dialogue of tensor-product types, multi-domain equipment, and preconditioners for iterative answer concepts. various discretizations of the regular and unsteady Stokes and Navier-Stokes equations are awarded, with specific sttention given to enforcement of imcompressibility. complicated discretizations. implementation matters, and parallel and vector functionality are thought of within the ultimate sections. quite a few examples are supplied all through to demonstrate the features of high-order equipment in real functions.

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Extra resources for High-order methods for incompressible fluid flow

Example text

From the numerical point of view, it is fairly easy in a finite-element method to construct a mixed model as a combination of two classical models. 10. Turbulence and Challenges 21 inside the computational domain, the k– model produces a full turbulence description. This approach is known as the two-layer model. Over the past decade, since the pioneering work of Yakhot and Orszag [416], renormalization group (RNG) theory has paved the way to new developments and generated extensive research to justify and complete the existing models.

From the begining, conjugate gradient ( CG) methods were suggested, since the system matrix is symmetric positive definite. It is well known that CG converges slowly, and thus the preconditioning issue is of vital importance. For one example, let us consider Legendre spectral elements as proposed by Maday and Patera [261] in 1989. When preconditioned by the diagonal, as is usually done, the system has a condition number O(E 12 N 2 ), where E 1 is the number of spectral elements in a typical spatial direction and E is the total number of spectral elements in the 3D problem.

Later in the book, we will present high-order methods to cope with such disadvantages. , collocation or spectral elements) are able to deal with complex geometries and complex 32 1. Fluid Mechanics and Computation: An Introduction boundary conditions and to treat singularities by mortar elements or domain decomposition. The use of high-order numerical techniques on massively parallel processing machines opens the door to many large-scale applications in computational science and engineering.

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High-order methods for incompressible fluid flow by Deville M.O., Fischer P.F., Mund E.H.

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