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- W4254752644 abstract "Over the last three decades, various upwinding types of finite element algorithms for fluid dynamics have been developed. The examples of these algorithms include Petrov–Galerkin and Galerkin least square methods. There are numerous versions of such methods available and several variants of such upwinding schemes are essentially similar or often identical to Petrov–Galerkin schemes. Over the last 15 years, I have been looking for some of the problems associated with this so-called upwinding methods. Majority of these methods are not suitable to carry out explicit or matrix-free calculations and also these methods are difficult to employ as a unified approach to both compressible and incompressible flows problems. In addition, incompressibility constraint needs to be explicitly imposed when these methods were used for nearly or fully incompressible flow problems. At the initial stages of search for better fluid dynamics algorithms, in Swansea, we developed the so-called Taylor Galerkin methods, a finite element version of the Lax Wendroff family. This method allowed us to carryout matrix-free and explicit calculations, but other mentioned problems were still unsolved. After several years of search, we finally concluded that the characteristic-based methods along with a Chorin-type split are the best choice which eliminates majority of the problems encountered by other algorithms. This was clearly realized by me and my co-workers and the first full-length paper was published in 1995. We have named the method ‘Characteristic-Based Split (CBS)’ algorithm in 1998/1999. Since introduction, this method has been employed to solve various engineering problems and being adopted by many. We now have an algorithm which is general, unified and as accurate as any other competing methods. This method has been employed in a variety of engineering problems including general compressible and incompressible flows, shallow-water flows, thermal flows, solid dynamics, porous medium flows and viscoelastic flows. Despite the significant progress made over the last decade, I believe that the message has not reached many active and would-be researchers. I believe that this special issue edited by P. Nithiarasu and R. Codina will reemphasize the point that we have a versatile and general purpose engineering algorithm to use. I am confident that the papers published in this issue will serve as a reference work over the years to come." @default.
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- W4254752644 date "2006-05-09" @default.
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- W4254752644 title "Foreword" @default.
- W4254752644 doi "https://doi.org/10.1002/nme.1688" @default.
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