{"title":"带分数阶拉普拉斯的曲面拟地转方程的点阵Boltzmann方法","authors":"Haoyuan Gong, Tongtong Zhou, Baochang Shi, Rui Du","doi":"10.1016/j.aml.2024.109434","DOIUrl":null,"url":null,"abstract":"The surface quasi-geostrophic equations with fractional Laplacian are important in the field of oceanic and atmospheric dynamics. In this paper, a new lattice Boltzmann model is proposed to solve the equations. We first obtain an approximation of the governing equation based on the Fourier transform and Gaussian quadrature formula. An LBGK model with a suitable equilibrium distribution function is then developed for the problem. Through Chapman–Enskog expansion, the approximated macroscopic equations can be recovered from the lattice Boltzmann model. Numerical simulations are carried out to verify the numerical accuracy and efficiency.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"1 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lattice Boltzmann method for surface quasi-geostrophic equations with fractional Laplacian\",\"authors\":\"Haoyuan Gong, Tongtong Zhou, Baochang Shi, Rui Du\",\"doi\":\"10.1016/j.aml.2024.109434\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The surface quasi-geostrophic equations with fractional Laplacian are important in the field of oceanic and atmospheric dynamics. In this paper, a new lattice Boltzmann model is proposed to solve the equations. We first obtain an approximation of the governing equation based on the Fourier transform and Gaussian quadrature formula. An LBGK model with a suitable equilibrium distribution function is then developed for the problem. Through Chapman–Enskog expansion, the approximated macroscopic equations can be recovered from the lattice Boltzmann model. Numerical simulations are carried out to verify the numerical accuracy and efficiency.\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1016/j.aml.2024.109434\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.aml.2024.109434","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Lattice Boltzmann method for surface quasi-geostrophic equations with fractional Laplacian
The surface quasi-geostrophic equations with fractional Laplacian are important in the field of oceanic and atmospheric dynamics. In this paper, a new lattice Boltzmann model is proposed to solve the equations. We first obtain an approximation of the governing equation based on the Fourier transform and Gaussian quadrature formula. An LBGK model with a suitable equilibrium distribution function is then developed for the problem. Through Chapman–Enskog expansion, the approximated macroscopic equations can be recovered from the lattice Boltzmann model. Numerical simulations are carried out to verify the numerical accuracy and efficiency.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.