Yang W, Li C. A Unified Lattice Boltzmann Model for Fourth Order Partial Differential Equations with Variable Coefficients.
ENTROPY (BASEL, SWITZERLAND) 2022;
24:1176. [PMID:
36141062 PMCID:
PMC9497726 DOI:
10.3390/e24091176]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Revised: 08/15/2022] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
In this work, a unified lattice Boltzmann model is proposed for the fourth order partial differential equation with time-dependent variable coefficients, which has the form ut+α(t)(p1(u))x+β(t)(p2(u))xx+γ(t)(p3(u))xxx+η(t)(p4(u))xxxx=0. A compensation function is added to the evolution equation to recover the macroscopic equation. Applying Chapman-Enskog expansion and the Taylor expansion method, we recover the macroscopic equation correctly. Through analyzing the error, our model reaches second-order accuracy in time. A series of constant-coefficient and variable-coefficient partial differential equations are successfully simulated, which tests the effectiveness and stability of the present model.
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