scholarly journals Enabling convergence of the iterated penalty Picard iteration with O(1) penalty parameter for incompressible Navier–Stokes via Anderson acceleration

2021 ◽  
Vol 387 ◽  
pp. 114178
Author(s):  
Leo G. Rebholz ◽  
Duygu Vargun ◽  
Mengying Xiao
Keyword(s):  
Picard Iteration ◽  
Navier Stokes ◽  
Penalty Parameter ◽  
Anderson Acceleration

Singularities

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Stokes Equations ◽  
Negative Answer ◽  
Three Dimensions ◽  
Picard Iteration ◽  
Navier Stokes ◽  
Scale Invariant ◽  
Navier Stokes Equations ◽  
L2 Norm ◽  
Two Dimensional Flow ◽  
Physical Consequences

The initial value problem of the incompressible Navier–Stokes equations is explained. Leray’s classic study of it (using Picard iteration) is simplified and described in the language of physics. The ideas of Lebesgue and Sobolev norms are explained. The L2 norm being the energy, cannot increase. This gives sufficient control to establish existence, regularity and uniqueness in two-dimensional flow. The L3 norm is not guaranteed to decrease, so this strategy fails in three dimensions. Leray’s proof of regularity for a finite time is outlined. His attempts to construct a scale-invariant singular solution, and modern work showing this is impossible, are then explained. The physical consequences of a negative answer to the regularity of Navier–Stokes solutions are explained. This chapter is meant as an introduction, for physicists, to a difficult field of analysis.

scholarly journals Acceleration of nonlinear solvers for natural convection problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sara Pollock ◽  
Leo G. Rebholz ◽  
Mengying Xiao
Keyword(s):  
Boussinesq Equations ◽  
Convergence Result ◽  
Newton Iteration ◽  
Picard Iteration ◽  
Boussinesq System ◽  
Solution Technique ◽  
Boussinesq Model ◽  
Robust Solution ◽  
Regularity Properties ◽  
Anderson Acceleration

AbstractThis paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing the fixed point operator associated with the nonlinear iteration to prove that certain stability and regularity properties hold, we apply the authors’ recently constructed theory for Anderson acceleration, which yields a convergence result for the Anderson accelerated Picard iteration for the Boussinesq system. The result shows that the leading term in the residual is improved by the gain in the optimization problem, but at the cost of additional higher order terms that can be significant when the residual is large. We perform numerical tests that illustrate the theory, and show that a 2-stage choice of Anderson depth can be advantageous. We also consider Anderson acceleration applied to the Newton iteration for the Boussinesq equations, and observe that the acceleration allows the Newton iteration to converge for significantly higher Rayleigh numbers that it could without acceleration, even with a standard line search.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Experimental and Numerical Analysis of a Motorcycle Air Intake System Aerodynamics and Performance

2020 ◽  
Vol 17 (1) ◽  
Author(s):  
M. A. Abd Halim ◽  
N. A. R. Nik Mohd ◽  
M. N. Mohd Nasir ◽  
M. N. Dahalan
Keyword(s):  
Combustion Process ◽  
Three Dimensional ◽  
Engine Performance ◽  
Internal Flow ◽  
Rapid Expansion ◽  
Navier Stokes ◽  
Turbulent Fluctuation ◽  
Ansys Fluent ◽  
Induction System ◽  
Acceleration And Deceleration

Induction system or also known as the breathing system is a sub-component of the internal combustion system that supplies clean air for the combustion process. A good design of the induction system would be able to supply the air with adequate pressure, temperature and density for the combustion process to optimizing the engine performance. The induction system has an internal flow problem with a geometry that has rapid expansion or diverging and converging sections that may lead to sudden acceleration and deceleration of flow, flow separation and cause excessive turbulent fluctuation in the system. The aerodynamic performance of these induction systems influences the pressure drop effect and thus the engine performance. Therefore, in this work, the aerodynamics of motorcycle induction systems is to be investigated for a range of Cubic Feet per Minute (CFM). A three-dimensional simulation of the flow inside a generic 4-stroke motorcycle airbox were done using Reynolds-Averaged Navier Stokes (RANS) Computational Fluid Dynamics (CFD) solver in ANSYS Fluent version 11. The simulation results are validated by an experimental study performed using a flow bench. The study shows that the difference of the validation is 1.54% in average at the total pressure outlet. A potential improvement to the system have been observed and can be done to suit motorsports applications.

Stress fields in granular material and implications for performance of robot locomotion over granular media

2015 ◽  
Vol 8 (1) ◽  
pp. 2005-2009
Author(s):  
Diandong Ren ◽  
Lance M. Leslie ◽  
Congbin Fu
Keyword(s):  
Mechanical Properties ◽  
Granular Material ◽  
Granular Media ◽  
Rotation Frequency ◽  
Legged Locomotion ◽  
Working Environment ◽  
Navier Stokes ◽  
Maximum Speed ◽  
Sigmoid Curve ◽  
Multi Body

 Legged locomotion of robots has advantages in reducing payload in contexts such as travel over deserts or in planet surfaces. A recent study (Li et al. 2013) partially addresses this issue by examining legged locomotion over granular media (GM). However, they miss one extremely significant fact. When the robot’s wheels (legs) run over GM, the granules are set into motion. Hence, unlike the study of Li et al. (2013), the viscosity of the GM must be included to simulate the kinematic energy loss in striking and passing through the GM. Here the locomotion in their experiments is re-examined using an advanced Navier-Stokes framework with a parameterized granular viscosity. It is found that the performance efficiency of a robot, measured by the maximum speed attainable, follows a six-parameter sigmoid curve when plotted against rotating frequency. A correct scaling for the turning point of the sigmoid curve involves the footprint size, rotation frequency and weight of the robot. Our proposed granular response to a load, or the ‘influencing domain’ concept points out that there is no hydrostatic balance within granular material. The balance is a synergic action of multi-body solids. A solid (of whatever density) may stay in equilibrium at an arbitrary depth inside the GM. It is shown that there exists only a minimum set-in depth and there is no maximum or optimal depth. The set-in depth of a moving robot is a combination of its weight, footprint, thrusting/stroking frequency, surface property of the legs against GM with which it has direct contact, and internal mechanical properties of the GM. If the vehicle’s working environment is known, the wheel-granular interaction and the granular mechanical properties can be grouped together. The unitless combination of the other three can form invariants to scale the performance of various designs of wheels/legs. Wider wheel/leg widths increase the maximum achievable speed if all other parameters are unchanged.

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