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Book Stabilization of a Time Integrator for the 3D Shallow Water Equations by Smoothing Techniques

Download or read book Stabilization of a Time Integrator for the 3D Shallow Water Equations by Smoothing Techniques written by Erik D. de Goede and published by . This book was released on 1989 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A smoothing technique is applied to improve the stability of a semi-implicit time integrator for the three-dimensional shallow water equations. In this method the vertical terms are treated implicitly. The stability condition on the time step only depends on the horizontal mesh sizes. Therefore, in horizontal direction an explicit smoothing operator is added. Due to the smoothing, the maximally stable time step increases considerably, while the accuracy is hardly affected. Moreover, it turns out that the explicit smoothing operator is efficient on any type of computer. In particular, the smoothing operator is very efficient on vector and parallel computers."

Book Scientific and Technical Aerospace Reports

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Book Report NM R

Download or read book Report NM R written by and published by . This book was released on 1984 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Monthly Weather Review

Download or read book Monthly Weather Review written by and published by . This book was released on 1991 with total page 1110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Numerical Methods for the 3D Shallow Water Equations on Vector and Parallel Computers

Download or read book Numerical Methods for the 3D Shallow Water Equations on Vector and Parallel Computers written by Erik D. de Goede and published by . This book was released on 1991 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The performance of both iteration methods is accelerated by a technique based on smoothing. Both explicit and implicit smoothing is examined. It turns out that the unconditionally stable method is more efficient than the conditionally stable methods."

Book CWI Quarterly

Download or read book CWI Quarterly written by and published by . This book was released on 1994 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Government reports annual index

Download or read book Government reports annual index written by and published by . This book was released on 199? with total page 1120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book 3D Modeling of Nonlinear Wave Phenomena on Shallow Water Surfaces

Download or read book 3D Modeling of Nonlinear Wave Phenomena on Shallow Water Surfaces written by Iftikhar B. Abbasov and published by John Wiley & Sons. This book was released on 2018-01-31 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: With climate change, erosion, and human encroachment on coastal environments growing all over the world, it is increasingly important to protect populations and environments close to the sea from storms, tsunamis, and other events that can be not just costly to property but deadly. This book is one step in bringing the science of protection from these events forward, the most in-depth study of its kind ever published. The analytic and numerical modeling problems of nonlinear wave activities in shallow water are analyzed in this work. Using the author's unique method described herein, the equations of shallow water are solved, and asymmetries that cannot be described by the Stokes theory are solved. Based on analytical expressions, the impacts of dispersion effects to wave profiles transformation are taken into account. The 3D models of the distribution and refraction of nonlinear surface gravity wave at the various coast formations are introduced, as well. The work covers the problems of numerical simulation of the run-up of nonlinear surface gravity waves in shallow water, transformation of the surface waves for the 1D case, and models for the refraction of numerical modeling of the run-up of nonlinear surface gravity waves at beach approach of various slopes. 2D and 3D modeling of nonlinear surface gravity waves are based on Navier-Stokes equations. In 2D modeling the influence of the bottom of the coastal zone on flooding of the coastal zone during storm surges was investigated. Various stages of the run-up of nonlinear surface gravity waves are introduced and analyzed. The 3D modeling process of the run-up is tested for the coast protection work of the slope type construction. Useful for students and veteran engineers and scientists alike, this is the only book covering these important issues facing anyone working with coastal models and ocean, coastal, and civil engineering in this area.

Book Applied mechanics reviews

Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Towards Efficient Techniques for Solutions of the Shallow Water Equations

Download or read book Towards Efficient Techniques for Solutions of the Shallow Water Equations written by Owen Thomas DeGennaro-Ransom and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Research was conducted in order to develop more efficient solution techniques for the Shallow Water Equations (SWE) for naturally occurring free-surface flows in natural and engineered channels. Methods relating to numerical solution of the two-dimensional equations utilizing graphical processing units (GPU) as the main computational device and combined one-and two-dimensional schemes are presented and tested. Different numerical methods were investigated for inclusion to the model. General requirements for the proposed schemes included the ability to be solved using a finite-difference conservative solution algorithm on a fixed rectangular grid and the ability to both withstand and provide reasonable approximation of shocks and bores within the solution domain. Two such schemes were investigated that met initial criteria: A graphical processing unit (GPU) implementation of the well established MacCormack method, and a selectively under-relaxed implicit method. Both methods included the addition of a TVD (total variation diminishing) term to help maintain stability around high gradient flow areas.The implicit method incorporates an algorithm for selectively under-relaxing the iterative process to maintain stability in the presence of shock interfaces. The value of the Courant number and the frequency at which the TVD term was incorporated were constantly updated during the computation to achieve optimal speed of execution while maintaining stability. The method was tested against published results from experiments and from computations employing alternative algorithms and the results obtained demonstrate both the economy and accuracy of the proposed algorithm. The MacCormack-based scheme was chosen for both optimizing procedure attempts. Methodology was tested that allowed for one and two-dimensional TVD-MacCormack equation coupling, reducing grid-size dependency for the solution domain, while permitting simultaneous calculation of both one and two dimensional domains, and the explicit, finite-difference formulation of the solution methodology was well suited for inclusion into simultaneous GPU calculation. Cell alignment and cell-neighbor management is shifted from matrix to array form, which allows for a new framework, optimally constructed for inclusion of the dimensionally coupled solution scheme. The code contains adaptive time-stepping, based on maximum local Courant number, and special wetting/drying schemes to maximize stability while maintaining accuracy. The method was tested against published results, showing it's effectiveness in minimizing computational resources while comparing well with experimentally derived results. The coupled code is tempered for insertion into a parallel computing array. Ultimately, while dimensional coupling provided a slight optimization in terms of computational efficiency, the dimensional interface methodology and limited domain types the solution technique was constructed for restrict it to a specific-use tool. The extension of the MacCormack method to GPU processing ultimately proved more useful, showing speed increases of 4-40 times depending on the domains geomorphological characteristics.

Book A Time Splitting Method for the Three dimensional Shallow Water Equations

Download or read book A Time Splitting Method for the Three dimensional Shallow Water Equations written by Erik D. de Goede and published by . This book was released on 1990 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The resulting method is mass conservative and efficient on vector and parallel computers. The accuracy, stability, and computational efficiency of this method is demonstrated for wind induced problems ina rectangular basis."

Book Variational Integrators for the Rotating Shallow Water Equations

Download or read book Variational Integrators for the Rotating Shallow Water Equations written by Rüdiger Brecht and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical simulation of the Earth's atmosphere plays an important role in developing our understanding of climate change. The atmosphere and ocean can be seen as a shallow fluid on the globe; here, we use the shallow water equations as a first step to approximate these geophysical flows. Then, the numerical model can only be accurate if it has good conservation properties, e.g. without conserving mass the simulation can not be physical. Obtaining such a numerical model can be achieved using numerical variational integration. Here, we have derived a numerical variational integrator for the rotating shallow water equations on the sphere using the Euler-Poincaré framework. First, the continuous Lagrangian is discretized; then, the numerical scheme is obtained by computing the discrete variational principle. The conservational properties and accuracy of the model are verified with standard test cases. However, in order to obtain more realistic simulations, the shallow water equations need to include physical parametrizations. Thus, we introduce a new representation of the rotating shallow water equations based on a stochastic transport principle. Then, benchmarks are carried out to demonstrate that the spatial part of the stochastic scheme preserves the total energy. The proposed random model better captures the structure of a large-scale flow than a comparable deterministic model. Furthermore, to be able to carry out long term simulations we extend the discrete Euler-Poincaré framework with a selective decay. The selective decay dissipates an otherwise conserved quantity while conserving energy. We apply the new framework to the shallow water equations to dissipate the potential enstrophy. Then, we carry out standard benchmarks to demonstrate the conservation properties. We show that the selective decay resolves more small scales compared to a standard dissipation.