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Book Compact Finite Difference Schemes for the Euler and Navier Stokes Equations

Download or read book Compact Finite Difference Schemes for the Euler and Navier Stokes Equations written by and published by . This book was released on 1982 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book An Upwind Method for the Solution of the 3D Euler and Navier Stokes Equations on Adaptively Meshes

Download or read book An Upwind Method for the Solution of the 3D Euler and Navier Stokes Equations on Adaptively Meshes written by Michael J. Aftosmis and published by . This book was released on 1992 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new node based upwind scheme for the solution of the 3D Navier- Stokes equations on adaptively refined meshes is presented. The method uses a second-order upwind TVD scheme to integrate the convective terms, and discretizes the viscous terms with a new compact central difference technique. Grid adaptation is achieved through directional division of hexahedral cells in response to evolving features as the solution converges. The method is advanced in time with a multistage Runge-Kutta time stepping scheme. Two- and three- dimensional examples establish the accuracy of the inviscid and viscous discretization. These investigations highlight the ability of the method to produce crisp shocks, while accurately and economically resolving viscous layers. The representation of these and other structures is shown to be comparable to that obtained by structured methods. Further 3D examples demonstrate the ability of the adaptive algorithm to effectively locate and resolve multiple scale features in complex 3D flows with many interacting, viscous, and inviscid structures.

Book Compact High Order Schemes for the Euler Equations

Download or read book Compact High Order Schemes for the Euler Equations written by Saul Abarbanel and published by . This book was released on 1988 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: An implicit approximate factorization (AF) algorithm is constructed which has the following characteristics. In 2-D: The scheme is unconditionally stable, has a 3 x 3 stencil and at steady state has a fourth order spatial accuracy. The temporal evolution is time accurate either to 1st or 2nd order through choice of parameter. In 3-D: The scheme has almost the same properties as in 2-D except that it is now only conditionally stable, with the stability condition (the CFL number) being dependent on the cell aspect ratios, Delta y/Delta x and Delta z/Delta x. The stencil is still compact and fourth order accuracy at steady state is maintained. Numerical experiments on a 2-D shock-reflection problem show the expected improvement over lower order schemes, not only in accuracy (measured by the L2 error) but also in the dispersion. It is also shown how the same technique is immediately extendable to Runge Kutta type schemes resulting in improved stability in addition to the enhanced accuracy. Keywords: Euler equations; Compact schemes; High order accuracy; Dispersion.

Book Boundary and Interface Conditions for Higher Order Finite Difference Methods Applied to the Euler and Navier Stokes Equations

Download or read book Boundary and Interface Conditions for Higher Order Finite Difference Methods Applied to the Euler and Navier Stokes Equations written by Jan Nordström and published by . This book was released on 1998 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book An Implicit Finite Difference Scheme for the Compressible Navier Stokes Equations

Download or read book An Implicit Finite Difference Scheme for the Compressible Navier Stokes Equations written by G. Degrez and published by . This book was released on 1987 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Navier stokes Equations In Planar Domains

Download or read book Navier stokes Equations In Planar Domains written by Matania Ben-artzi and published by World Scientific. This book was released on 2013-03-07 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as “driven cavity” and “double-driven cavity”.A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a “pure streamfunction” approach. In particular, a complete proof of convergence is given for the full nonlinear problem.This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics./a

Book Fundamentals of Computational Fluid Dynamics

Download or read book Fundamentals of Computational Fluid Dynamics written by H. Lomax and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chosen semi-discrete approach of a reduction procedure of partial differential equations to ordinary differential equations and finally to difference equations gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.

Book Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations

Download or read book Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations written by Geeta Arora and published by CRC Press. This book was released on 2024-01-23 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. Models guided by differential equations with intuitive solutions can be used throughout engineering and the sciences. Almost any changing system may be described by a set of differential equations. They may be found just about anywhere you look in fields including physics, engineering, economics, sociology, biology, business, healthcare, etc. The nature of these equations has been investigated by several mathematicians over the course of hundreds of years and, consequently, numerous effective methods for solving them have been created. It is often impractical to find a purely analytical solution to a system described by a differential equation because either the system itself is too complex or the system being described is too vast. Numerical approaches and computer simulations are especially helpful in such systems. The content provided in this book involves real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems. Theories and practical applications in the sciences and engineering are also discussed. Students of engineering and applied mathematics, as well as researchers and engineers who use computers to solve problems numerically or oversee those who do, will find this book focusing on advance numerical techniques to solve linear and nonlinear differential equations useful.

Book Analysis of Finite Difference Schemes for the Time Dependent Stokes Equtions

Download or read book Analysis of Finite Difference Schemes for the Time Dependent Stokes Equtions written by Young S. Lee and published by . This book was released on 1998 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Finite Difference Methods for the Stokes and Navier Stokes Equations

Download or read book Finite Difference Methods for the Stokes and Navier Stokes Equations written by John C. Strikwerda and published by . This book was released on 1982 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a new finite difference scheme for the Stokes equations and incompressible Navier-Stokes equations for low Reynold's number. The scheme uses the primitive variable formulation of the equations and is applicable with non-uniform grids and non-rectangular geometries. Several other methods of solving the Navier-Stokes equations are also examined in this paper and some of their strengths and weaknesses are described. Computational results using the new scheme are presented for the Stokes equations for a region with curved boundaries and for a disc with polar coordinates. The results show the method to be second-order accurate. (Author).