Modal Approximation

2011 ◽  
pp. 145-157
Author(s):  
Krešimir Veselić
Keyword(s):  
Modal Approximation

Development of a New Simulation Technique Based on the Modal Approximation for Fluid Transients in Complex Pipeline Systems With Time-Variant Nonlinear Boundary Conditions

2006 ◽  
Vol 129 (6) ◽  
pp. 791-798 ◽  
Author(s):  
E. Kojima ◽  
T. Yamazaki ◽  
M. Shinada
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Safety Valve ◽  
Nonlinear Boundary Conditions ◽  
Simulation Technique ◽  
Nonlinear Relationship ◽  
Calculation Methods ◽  
Pipeline Systems ◽  
Fluid Transients ◽  
Modal Approximation

A new simulation technique called the system modal approximation method (SMA) for fluid transients in complex pipeline systems has been proposed. The superiority of this technique compared to other existing methods has been verified. Thus far, however, detailed considerations have been limited to pipelines having elementary boundary conditions. In the present paper, for the generalization of the SMA method, calculation methods are newly proposed for the case in which the boundary conditions are given by the time-variant nonlinear relationship between pressure and flow rate, such as the conditions in a safety valve, and its usefulness is verified by comparison to experimental measurements.

Modal Approximation Formulas for Shallow Water Waveguides (March 2007)

2007 ◽  
Author(s):  
Stephen V. Kaczkowski ◽  
Allan D. Pierce ◽  
William M. Carey ◽  
William L. Siegmann
Keyword(s):  
Shallow Water ◽  
Approximation Formulas ◽  
Modal Approximation

scholarly journals Modal approximation for plasmonic resonators in the time domain: the scalar case

2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Lorenzo Baldassari ◽  
Pierre Millien ◽  
Alice L. Vanel
Keyword(s):  
Time Domain ◽  
Homogeneous Medium ◽  
Low Frequency ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Scalar Case ◽  
Singular Boundary ◽  
Metallic Nanoparticle ◽  
The Time Domain ◽  
Modal Approximation

AbstractWe study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters in a resonant regime. We consider the particle placed in a homogeneous medium in a low-frequency regime. We define modes for the non-Hermitian problem as perturbations of electro-static modes, and obtain a modal approximation of the scattered field in the frequency domain. The poles of the expansion correspond to the eigenvalues of a singular boundary integral operator and are shown to lie in a bounded region near the origin of the lower-half complex plane. Finally, we show that this modal representation gives a very good approximation of the field in the time domain. We present numerical simulations in two dimensions to corroborate our results.

Dissipative Modal Approximation of Fluid Transmission Lines Using Linear Friction Model

1991 ◽  
Vol 113 (1) ◽  
pp. 152-162 ◽  
Author(s):  
W. C. Yang ◽  
W. E. Tobler
Keyword(s):  
Transmission Lines ◽  
Friction Model ◽  
Step Response ◽  
Frequency Dependent ◽  
Approximation Techniques ◽  
Linear Friction ◽  
Computer Calculations ◽  
Complex Fluid ◽  
Dependent Viscosity ◽  
Modal Approximation

For both hydraulic and pneumatic transmission lines, analytical dissipative modal approximation techniques, which take into account the frequency dependent viscosity and heat transfer effects, are developed by introducing frequency dependent damping and natural frequency modification factors to the quadratic modes obtained analytically from linear friction model. The main advantage over the existing dissipative modal approximations is that the modal parameters of the resulting modal transfer function matrices and modal state space equations can be determined analytically rather than determined by table and/or numerical computer calculations. This introduces modeling flexibilities and greatly alleviates the difficulties of modeling complex fluid networks but still maintaining the modal accuracy and complexities. Unit step response comparisons are made with quasi-method of characteristics showing good agreements for both hydraulic and pneumatic lines.

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