Introducing unsteady and nonuniform source terms in entropic lattice kinetic models using Fourier series

Khazaeli, Reza; Nazari, Mohammad Reza; Zadehgol, Abed

doi:10.1103/physreve.98.053303

Cited by 4 publications

(1 citation statement)

References 54 publications

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“…The FS is a branch of Fourier analysis nowadays. The FS has been applied to almost all disciplines, including physics [4] [5], architectonics [6] [7], electronics [8] [9], electrical engineering [10] [11] [12], and signal processing [13] [14] [15].…”

Section: Introductionmentioning

confidence: 99%

A Biproportional Construction Algorithm for Correctly Calculating Fourier Series of Aperiodic Non-Sinusoidal Signal

Li¹,

Ren²,

Chen³

2021

ENG

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The Fourier series (FS) applies to a periodic non-sinusoidal function satisfying the Dirichlet conditions, whereas the being-processed function ( ) f t in practical applications is usually an aperiodic non-sinusoidal signal. When ( ) f t is aperiodic, its calculated FS is not correct, which is still a challenging problem. To overcome the problem, we derive a direct calculation algorithm, a constant iteration algorithm, and an optimal iteration algorithm. The direct calculation algorithm correctly calculates its Fourier coefficients (FCs) when ( ) f t is periodic and satisfies the Dirichlet conditions. Both the constant iteration algorithm and the optimal iteration algorithm provide an idea of determining the states of ( ) f t . From the idea, we obtain an algorithm for determining the states of ( ) f t based on the optimal iteration algorithm. In the algorithm, the variable iteration step is introduced; thus, we present an algorithm for determining the states of ( ) f t based on the variable iteration step. The presented algorithm accurately determines the states of ( ) f t . On the basis of these algorithms, we build a biproportional construction theory. The theory consists of a first and a second proportional construction theory. The former correctly calculates the FCs of ( ) f t at the present sampling time, and the latter creates a precondition for correctly calculating the FCs of ( ) f t at the next sampling time. From the biproportional construction theory, we propose a biproportional construction algorithm. The proposed biproportional construction algorithm correctly calculates its FCs whether ( ) f t is periodic or aperiodic, and thus its FS.

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