A mass-conserved multiphase lattice Boltzmann method based on high-order difference<xref rid="cpb_29_3_034701fn1" ref-type="fn">*</xref><fn id="cpb_29_3_034701fn1"><label>*</label><p>Project supported by the National Natural Science Foundation of China (Grant Nos. 11862003 and 81860635), the Key Project of the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2017GXNSFDA198038), the Project of Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2018GXNSFAA281302), the Project for Promotion of Young and Middle-aged Teachers’ Basic Scientific Research Ability in Guangxi Universities, China (Grant No. 2019KY0084), and the “Bagui Scholar” Teams for Innovation and Research Project of Guangxi Zhuang Autonomous Region, China, and the Graduate Innovation Program of Guangxi Normal University, China (Grant No. JXYJSKT-2019-007).</p></fn>

A mass-conserved multiphase lattice Boltzmann method based on high-order difference**

Project supported by the National Natural Science Foundation of China (Grant Nos. 11862003 and 81860635), the Key Project of the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2017GXNSFDA198038), the Project of Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2018GXNSFAA281302), the Project for Promotion of Young and Middle-aged Teachers’ Basic Scientific Research Ability in Guangxi Universities, China (Grant No. 2019KY0084), and the “Bagui Scholar” Teams for Innovation and Research Project of Guangxi Zhuang Autonomous Region, China, and the Graduate Innovation Program of Guangxi Normal University, China (Grant No. JXYJSKT-2019-007).

Qin Zhang-Rong, Chen Yan-Yan, Ling Feng-Ru, Meng Ling-Juan, Zhang Chao-Ying^†

Evolutions of rising bubble mass with time in four cases (C1)–(C4).