{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T05:03:31Z","timestamp":1692335011064},"reference-count":16,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,17]],"date-time":"2023-08-17T00:00:00Z","timestamp":1692230400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National College Student Innovation and Entrepreneurship Training Program","award":["202210755091"]},{"name":"NSF of China","award":["12001466"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"A novel dimension splitting method is proposed for the efficient numerical simulation of a biochemotaxis model, which is a coupled system of chemotaxis\u2013fluid equations and incompressible Navier\u2013Stokes equations. A second-order pressure correction method is employed to decouple the velocity and pressure for the Navier\u2013Stokes equations. Then, the alternating direction implicit scheme is used to solve the velocity equation, and the operator with dimension splitting effect is used instead of the traditional elliptic operator to solve the pressure equation. For the chemotactic equation, the operator splitting method and extrapolation technique are used to solve oxygen and cell density to achieve second-order time accuracy. The proposed dimension splitting method splits the two-dimensional problem into a one-dimensional problem by splitting the spatial derivative, which reduces the computation and storage costs. Finally, through interesting experiments, we show the evolution of the cell plume shape during the descent process. The effect of changing specific parameters on the velocity and plume shape during the descent process is also studied.<\/jats:p>","DOI":"10.3390\/e25081224","type":"journal-article","created":{"date-parts":[[2023,8,17]],"date-time":"2023-08-17T14:15:48Z","timestamp":1692281748000},"page":"1224","source":"Crossref","is-referenced-by-count":0,"title":["Efficient Numerical Simulation of Biochemotaxis Phenomena in Fluid Environments"],"prefix":"10.3390","volume":"25","author":[{"given":"Xingying","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Future Technology, Xinjiang University, Urumqi 830046, China"}]},{"given":"Guoqing","family":"Bian","sequence":"additional","affiliation":[{"name":"School of Future Technology, Xinjiang University, Urumqi 830046, China"}]},{"given":"Yan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}]},{"given":"Xufeng","family":"Xiao","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/0092-8240(94)00038-E","article-title":"The development of concentration gradients in a suspension of chemotactic bacteria","volume":"57","author":"Hillesdon","year":"1995","journal-title":"Bull. 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Fluid Mech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/s002850000038","article-title":"Fractional step methods applied to a chemotaxis model","volume":"41","author":"Tyson","year":"2000","journal-title":"J. Math. Biol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s00211-008-0188-0","article-title":"A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models","volume":"111","author":"Chertock","year":"2008","journal-title":"Numer. Math."},{"key":"ref_7","first-page":"341","article-title":"A diffuse-domain based numerical method for a Chemotaxis-Fluid model","volume":"33","author":"Wang","year":"2022","journal-title":"Numer. Anal."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Morton, K.W., and Mayers, D.F. (2005). Numerical Solution of Partial Differential Equations: An introduction, Cambridge University Press.","DOI":"10.1017\/CBO9780511812248"},{"key":"ref_9","unstructured":"Thomas, J.W. (2013). Numerical Partial Differential Equations: Finite Difference Methods, Springer Science & Business Media."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3128","DOI":"10.1016\/j.camwa.2019.01.023","article-title":"Operator-splitting methods for the 2D convective Cahn-Hilliard equation","volume":"77","author":"Gidey","year":"2019","journal-title":"Comput. Math. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.physa.2015.03.012","article-title":"A second order operator splitting method for Allen-Cahn type equations with nonlinear source terms","volume":"432","author":"Lee","year":"2015","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.jcp.2015.06.038","article-title":"First and second order operator splitting methods for the phase field crystal equation","volume":"299","author":"Lee","year":"2015","journal-title":"J. Comput. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1016\/j.cma.2011.02.007","article-title":"A new class of massively parallel direction splitting for the incompressible Navier-Stokes equations","volume":"200","author":"Guermond","year":"2011","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"111412","DOI":"10.1016\/j.jcp.2022.111412","article-title":"A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations","volume":"466","author":"Chen","year":"2022","journal-title":"J. Comput. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1016\/j.compfluid.2007.10.006","article-title":"The MAC method","volume":"37","author":"McKee","year":"2008","journal-title":"Comput. Fluids"},{"key":"ref_16","first-page":"817","article-title":"Normal mode analysis of second-order projection methods for incompressible flows","volume":"5","author":"Pyo","year":"2005","journal-title":"Discret. Contin. Dyn. Syst. 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