Detonation Initiation on the Microsecond Time Scale: One and Two Dimensional Results Obtained from Adaptive Wavelet-Collocation Numerical Methods

2007 ◽  
Author(s):  
David Kassoy ◽  
J. Regele ◽  
O. Vasilyev
Keyword(s):  
Numerical Methods ◽  
Time Scale ◽  
Detonation Initiation ◽  
Two Dimensional ◽  
Adaptive Wavelet

A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

2015 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Schrödinger Equation ◽  
Computational Efficiency ◽  
Schrodinger Equation ◽  
Computational Cost ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
One Dimensional ◽  
Grid Adaptation ◽  
Adaptive Wavelet Method

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

scholarly journals Numerical hydrodynamic researches for justifying design of the Nizhny Novgorod low-head hydraulic system

2019 ◽  
pp. 3-3
Author(s):  
Anna Glotko ◽  
Vitalii Belikov ◽  
Natalia Borisova ◽  
Ekaterina Vasil`eva ◽  
Aleksey Rumjancev
Keyword(s):  
Numerical Methods ◽  
Hydraulic System ◽  
Problem Area ◽  
Low Flow ◽  
Hydroelectric Power Station ◽  
Two Dimensional ◽  
Hydroelectric Power ◽  
Flow Conditions ◽  
Power Station ◽  
Low Head

Introduction. A problem area of the Volga river between the Nizhny Novgorod hydroelectric power station and the city of Nizhny Novgorod has been surveyed, where unfavourable conditions for navigation, power generation, and safe living in the downstream are formed as a result of the landing level. The only solution to the problem is construction of a low-head hydraulic system (NNGU) that will reduce intensity of relief re-formations in the downstream of the Nizhny Novgorod hydraulic system and stop lowering of the bottom and level marks in this area. Purpose of this research is to study processes that occur upstream and downstream from the site of the facility to identify hazardous trends and develop practical solutions to minimize negative impacts; as well as a review of mathematical models conducted in this area for improving navigation conditions. Materials and methods. Materials of previous researches on this subject, pre-design engineering surveys and layout drawings of the designed hydraulic system are used. The researches have been performed with numerical methods using Stream 2D software package that is based on the two-dimensional differential equation Saint-Venant system. Options for low-flow conditions are considered, taking into account passing of the Nizhny Novgorod hydroelectric power station, as well as rare floods. Results. Plans for distribution of velocity modules and vectors are created, which show that construction of the low-pressure hydraulic system results in decrease in slopes and velocities of water in the problem area of the Volga-Kama cascade, as a result of which intensity of bottom deformations decreases. Rare flow passage demonstrated that difference in pools is insignificant, while, at the same time, flow of water along the left-bank floodplain passes more than believed before. Calculations of low-flow conditions demonstrated a number of deficiencies in the design, which are associated with insufficient throughput and uneven distribution of flow rates in the discharge area of the waterfront. Conclusion The results demonstrated a practical importance of using mathematical simulation with numerical methods in a two-dimensional formulation, which allow us to consider processes in more detailed manner and change the hydraulic system design in a timely manner.

Improved Two-Dimensional Dynamic Stall Prediction with Structured and Hybrid Numerical Methods

2011 ◽  
Vol 56 (4) ◽  
pp. 1-12 ◽  
Author(s):  
K. Richter ◽  
A. Le Pape ◽  
T. Knopp ◽  
M. Costes ◽  
V. Gleize ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
High Speed ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Boundary Layer Transition ◽  
Dynamic Stall ◽  
Two Dimensional ◽  
Layer Transition ◽  
The Impact

A joint comprehensive validation activity on the structured numerical method elsA and the hybrid numerical method TAU was conducted with respect to dynamic stall applications. To improve two-dimensional prediction, the influence of several factors on the dynamic stall prediction was investigated. The validation was performed for three deep dynamic stall test cases of the rotor blade airfoil OA209 against experimental data from two-dimensional pitching airfoil experiments, covering low-speed and high-speed conditions. The requirements for spatial discretization and for temporal resolution in elsA and TAU are shown. The impact of turbulence modeling is discussed for a variety of turbulence models ranging from one-equation Spalart–Allmaras-type models to state-of-the-art, seven-equation Reynolds stress models. The influence of the prediction of laminar/turbulent boundary layer transition on the numerical dynamic stall simulation is described. Results of both numerical methods are compared to allow conclusions to be drawn with respect to an improved prediction of dynamic stall.

scholarly journals Limiting stress states in granular avalanches

1998 ◽  
Vol 26 ◽  
pp. 272-276 ◽  
Author(s):  
Y.C. Tai ◽  
J.M.N.T. Gray
Keyword(s):  
Stress State ◽  
Numerical Methods ◽  
Granular Material ◽  
Laboratory Experiments ◽  
Complex Geometry ◽  
The Other ◽  
Two Dimensional ◽  
Singular Surfaces ◽  
Rapid Convergence ◽  
Stress States

The Savage-Hutter theory for granular avalanches assumes that the granular material is in either of two limiting stress states, depending on whether the motion is convergent or divergent. At transitions between convergent and divergent regions, a jump in stress occurs, which necessarily implies that there is a jump in the avalanche velocity and/or its thickness. In this paper, a regularizaron scheme is used, which smoothly switches from one stress state to the other, and avoids the generation of such singular surfaces. The resulting algorithm is more stable than previous numerical methods but shocks can still occur during rapid convergence in the run-out zone. Results are presented from two-dimensional calculations on complex geometry which illustrate that some necking features observed in laboratory experiments can be explained by the regularized Savage-Hutter model.

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