Multiple-Scales Method and Numerical Simulation of Singularly Perturbed Boundary Layer Problems

2016 ◽  
Vol 10 (3) ◽  
pp. 1119-1127
Author(s):  
Parul Gupta ◽  
Manoj Kumar
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Multiple Scales ◽  
Multiple Scales Method ◽  
Singularly Perturbed ◽  
Boundary Layer Problems

MATHEMATICAL MODELING OF QUINTIC DUFFING EQUATION AND NUMERICAL SIMULATION USING MULTIPLE SCALES MODIFIED LINDSTEDT–POINCARE METHOD

2012 ◽  
Vol 03 (04) ◽  
pp. 1250014
Author(s):  
MANOJ KUMAR ◽  
PARUL
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Approximate Solution ◽  
Closed Form ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Duffing Equation ◽  
Multiple Scales Method ◽  
Wide Range

A perturbation algorithm Multiple Scales Modified Lindstedt–Poincare (MSMLP), combination of method of Multiple Scales and modified Lindstedt–Poincare is proposed for the solution of Quintic Duffing equation which combines the advantages of both the methods. Solution obtained by the MSMLP method is compared with the Multiple Scales method and accurate closed form approximate solution of the Quintic Duffing equation. The proposed method produces better results for a wide range of amplitude values of oscillations and strong nonlinearities. Numerical simulation has been performed in MATHEMATICA 7.0.

scholarly journals A comparison between MMAE and SCEM for solving singularly perturbed linear boundary layer problems

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2135-2148
Author(s):  
Süleyman Cengizci
Keyword(s):  
Boundary Layer ◽  
Asymptotic Expansions ◽  
Present Method ◽  
Numerical Experiments ◽  
Expansion Method ◽  
Singularly Perturbed ◽  
Linear Boundary ◽  
Point Boundary ◽  
Matching Process ◽  
Boundary Layer Problems

In this study, we propose an efficient method so-called Successive Complementary Expansion Method (SCEM), that is based on generalized asymptotic expansions, for approximating to the solutions of singularly perturbed two-point boundary value problems. In this easy-applicable method, in contrast to the well-known method the Method of Matched Asymptotic Expansions (MMAE), any matching process is not required to obtain uniformly valid approximations. The key point: A uniformly valid approximation is adopted first, and complementary functions are obtained imposing the corresponding boundary conditions. An illustrative and two numerical experiments are provided to show the implementation and numerical properties of the present method. Furthermore, MMAE results are also obtained in order to compare the numerical robustnesses of the methods.

scholarly journals Development of Depth-Limited Wave Boundary Layers over a Smooth Bottom

2020 ◽  
Vol 9 (1) ◽  
pp. 27
Author(s):  
Hitoshi Tanaka ◽  
Nguyen Xuan Tinh ◽  
Xiping Yu ◽  
Guangwei Liu
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Wave Motion ◽  
Numerical Study ◽  
Experiment Data ◽  
Tidal Motion ◽  
Long Period ◽  
Simulation Results ◽  
Wave Boundary

A theoretical and numerical study is carried out to investigate the transformation of the wave boundary layer from non-depth-limited (wave-like boundary layer) to depth-limited one (current-like boundary layer) over a smooth bottom. A long period of wave motion is not sufficient to induce depth-limited properties, although it has simply been assumed in various situations under long waves, such as tsunami and tidal currents. Four criteria are obtained theoretically for recognizing the inception of the depth-limited condition under waves. To validate the theoretical criteria, numerical simulation results using a turbulence model as well as laboratory experiment data are employed. In addition, typical field situations induced by tidal motion and tsunami are discussed to show the usefulness of the proposed criteria.

scholarly journals Numerical Simulation about Reconstruction of the Boundary Layer

Energies ◽  
2017 ◽  
Vol 10 (12) ◽  
pp. 2074
Author(s):  
Yan Li ◽  
Chuan Li ◽  
Yajie Wu ◽  
Cong Liu ◽  
Han Yuan ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer
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