6,610 research outputs found
An efficient null space inexact Newton method for hydraulic simulation of water distribution networks
Null space Newton algorithms are efficient in solving the nonlinear equations
arising in hydraulic analysis of water distribution networks. In this article,
we propose and evaluate an inexact Newton method that relies on partial updates
of the network pipes' frictional headloss computations to solve the linear
systems more efficiently and with numerical reliability. The update set
parameters are studied to propose appropriate values. Different null space
basis generation schemes are analysed to choose methods for sparse and
well-conditioned null space bases resulting in a smaller update set. The Newton
steps are computed in the null space by solving sparse, symmetric positive
definite systems with sparse Cholesky factorizations. By using the constant
structure of the null space system matrices, a single symbolic factorization in
the Cholesky decomposition is used multiple times, reducing the computational
cost of linear solves. The algorithms and analyses are validated using medium
to large-scale water network models.Comment: 15 pages, 9 figures, Preprint extension of Abraham and Stoianov, 2015
(https://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001089), September 2015.
Includes extended exposition, additional case studies and new simulations and
analysi
Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows
In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids
Fast Neural Network Predictions from Constrained Aerodynamics Datasets
Incorporating computational fluid dynamics in the design process of jets,
spacecraft, or gas turbine engines is often challenged by the required
computational resources and simulation time, which depend on the chosen
physics-based computational models and grid resolutions. An ongoing problem in
the field is how to simulate these systems faster but with sufficient accuracy.
While many approaches involve simplified models of the underlying physics,
others are model-free and make predictions based only on existing simulation
data. We present a novel model-free approach in which we reformulate the
simulation problem to effectively increase the size of constrained pre-computed
datasets and introduce a novel neural network architecture (called a cluster
network) with an inductive bias well-suited to highly nonlinear computational
fluid dynamics solutions. Compared to the state-of-the-art in model-based
approximations, we show that our approach is nearly as accurate, an order of
magnitude faster, and easier to apply. Furthermore, we show that our method
outperforms other model-free approaches
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