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Fast and Accurate Methods for Predic...

Fang, Rui,

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Fast and Accurate Methods for Predicting Fluid Flows /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fast and Accurate Methods for Predicting Fluid Flows // Rui Fang.
Author:	Fang, Rui,
Description:	1 electronic resource (193 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 87-02, Section: B.
Contained By:	Dissertations Abstracts International87-02B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32170276
ISBN:	9798291570616

Fast and Accurate Methods for Predicting Fluid Flows /
Fang, Rui,

Fast and Accurate Methods for Predicting Fluid Flows /Rui Fang. - 1 electronic resource (193 pages)

Source: Dissertations Abstracts International, Volume: 87-02, Section: B.

Fluids in motion exhibit complex behaviors that are difficult to predict yet critical to applications such as renewable energy and weather forecasting. The Navier-Stokes equations (NSE) form the foundational mathematical model for nearly all fluid flows. For incompressible flows, pressure acts as a Lagrange multiplier enforcing the divergence-free constraint on velocity, which results in a coupled system.Due to the chaotic nature of fluid flow, small errors in initial conditions can grow exponentially fast in time, leading to finite predictability horizons. To address uncertainties in problem data, ensemble methods run simulations over a range of initial and boundary conditions. While ensembles improve prediction, they are computationally expensive, requiring solving J separate systems at each time step for an ensemble of size J.Chapter 1 introduces the challenges in fluid dynamics and the motivation for developing efficient numerical methods. Chapter 2 reviews chaos theory, predictability in dynamical systems, and ensemble forecasting.Chapter 3 develops a penalty-based ensemble method that reduces computational cost by using a shared coefficient matrix across ensemble members and relaxing the incompressibility condition. This approach decouples pressure from velocity, eliminates pressure variables, and lowers memory and computational costs while maintaining accuracy.The velocity error is sensitive to the choice of the penalty parameter, and no effective a priori formula exists. Chapter 4 extends Xie's adaptive penalty method for the Stokes problem to the nonlinear, time-dependent NSE. The method chooses the penalty parameter elementwise, adapting to the local divergence error. We give a comprehensive theoretical analysis.Direct numerical simulation is often impractical because of its need for fine spatial and temporal resolution. Unsteady Reynolds-averaged Navier-Stokes models provide a practical alternative. Chapter 5 studies a 1/2-equation model that simplifies the standard 1-equation turbulence model. We replace the partial differential equation for turbulent kinetic energy k(x, t) with its spatial average. This method reduces complexity to that of a 0-equation model while maintaining the accuracy of the 1-equation model. Chapter 6 studies the numerical analysis of the 1/2-equation model, including uniqueness for strong solutions, stability, convergence, and error estimates.

English

ISBN: 9798291570616Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Navier-Stokes equations

Fast and Accurate Methods for Predicting Fluid Flows /
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520 $a Fluids in motion exhibit complex behaviors that are difficult to predict yet critical to applications such as renewable energy and weather forecasting. The Navier-Stokes equations (NSE) form the foundational mathematical model for nearly all fluid flows. For incompressible flows, pressure acts as a Lagrange multiplier enforcing the divergence-free constraint on velocity, which results in a coupled system.Due to the chaotic nature of fluid flow, small errors in initial conditions can grow exponentially fast in time, leading to finite predictability horizons. To address uncertainties in problem data, ensemble methods run simulations over a range of initial and boundary conditions. While ensembles improve prediction, they are computationally expensive, requiring solving J separate systems at each time step for an ensemble of size J.Chapter 1 introduces the challenges in fluid dynamics and the motivation for developing efficient numerical methods. Chapter 2 reviews chaos theory, predictability in dynamical systems, and ensemble forecasting.Chapter 3 develops a penalty-based ensemble method that reduces computational cost by using a shared coefficient matrix across ensemble members and relaxing the incompressibility condition. This approach decouples pressure from velocity, eliminates pressure variables, and lowers memory and computational costs while maintaining accuracy.The velocity error is sensitive to the choice of the penalty parameter, and no effective a priori formula exists. Chapter 4 extends Xie's adaptive penalty method for the Stokes problem to the nonlinear, time-dependent NSE. The method chooses the penalty parameter elementwise, adapting to the local divergence error. We give a comprehensive theoretical analysis.Direct numerical simulation is often impractical because of its need for fine spatial and temporal resolution. Unsteady Reynolds-averaged Navier-Stokes models provide a practical alternative. Chapter 5 studies a 1/2-equation model that simplifies the standard 1-equation turbulence model. We replace the partial differential equation for turbulent kinetic energy k(x, t) with its spatial average. This method reduces complexity to that of a 0-equation model while maintaining the accuracy of the 1-equation model. Chapter 6 studies the numerical analysis of the 1/2-equation model, including uniqueness for strong solutions, stability, convergence, and error estimates.
546 $a English
590 $a School code: 0178
650 4 $a Mathematics. $3 515831
650 4 $a Applied mathematics. $3 2122814
650 4 $a Fluid mechanics. $3 528155
650 4 $a Mechanical engineering. $3 649730
653 $a Navier-Stokes equations
653 $a Renewable energy
653 $a Fluid flows
653 $a Dynamical systems
653 $a Lagrange multiplier enforcing
690 $a 0405
690 $a 0364
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710 2 $a University of Pittsburgh. $b Mathematics. $e degree granting institution. $3 3825878
720 1 $a Layton, William J. $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 87-02B.
790 $a 0178
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32170276