Analytical and numerical studies of the boundary slip in the immersed boundary‐thermal lattice Boltzmann method

Seta Takashi; Hayashi Kosuke; Tomiyama Akio

摘要

Summary >We analytically and numerically investigate the boundary slip, including the velocity slip and the temperature jump, in immersed boundary‐thermal lattice Boltzmann methods (IB‐TLBMs) with the two‐relaxation‐time collision operator. We derive the theoretical equation for the relaxation parameters considering the effect of the advection velocity on the temperature jump of the IB‐TLBMs. The analytical and numerical solutions demonstrate that the proposed iterative correction methods without the computational cost of the sparse matrix solver reduce the boundary slip and boundary‐value deviation as effectively as the implicit correction method for any relaxation time. Because the commonly used multi‐direct forcing method does not consider the contributions of the body force to the momentum flux, it cannot completely eliminate the boundary slip because of the numerical instability for a long relaxation time. Both types of proposed iterative correction methods are more numerically stable than the implicit correction method. In simulations of flow past a circular cylinder and of natural convection, the present iterative correction methods yield adequate results without the errors of the velocity slip, the temperature jump, and the boundary‐value deviation for any relaxation time parameters and for any number of Lagrangian points per length. The combination of the present methods and the two‐relaxation‐time collision operator is suitable for simulating fluid flow with thermal convection in the multiblock method in which the relaxation time increases in inverse proportion to the grid size. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”xml：id =“fld4462-abs-0001”xml：lang =“en”> <标题类型=“main” >摘要</标题> >我们分析并在用双弛豫时间碰撞运算符浸入边界 - 热格螺栓玻璃法（IB-TLBMS）中的边界滑动，包括速度滑动，包括速度滑移和温度跳跃。考虑到平流速度对IB-TLBMS的温度跳跃的影响，我们导出了放松参数的理论方程。分析和数值解决方案表明，没有稀疏矩阵求解器的计算成本的所提出的迭代校正方法减少了边界滑动和边界值偏差，作为任何松弛时间的隐式校正方法。由于常用的多直接强制方法不考虑体力对动量通量的贡献，因此由于长度放松时间的数值不稳定性，它不能完全消除边界滑动。两种类型的迭代校正方法比隐式校正方法更稳定。在流过圆柱和自然对流的流动模拟中，目前的迭代校正方法不会产生足够的结果而没有速度滑移，温度跳跃和任何弛豫时间参数的边界值偏差以及任何数量的拉格朗日的误差每个长度点。本方法和双弛豫时间碰撞运算符的组合适用于在多块方法中模拟流体流动，其中弛豫时间与网格尺寸相反地增加。</ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-20811/'>《International Journal for Numerical Methods in Fluids》</a> <b style="margin: 0 2px;">|</b><span>2018年第7期</span><b style="margin: 0 2px;">|</b><span>共37页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Seta Takashi&option=202" target="_blank" rel="nofollow">Seta Takashi;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Hayashi Kosuke&option=202" target="_blank" rel="nofollow">Hayashi Kosuke;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Tomiyama Akio&option=202" target="_blank" rel="nofollow">Tomiyama Akio;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Graduate School of Science and Engineering for ResearchUniversity of ToyamaToyama 930‐8555 Japan;</p> <p>Graduate School of EngineeringKobe UniversityHyogo 657‐8501 Japan;</p> <p>Graduate School of EngineeringKobe UniversityHyogo 657‐8501 Japan;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1155.html" title="流体力学">流体力学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=double‐population approach&option=203" rel="nofollow">double‐population approach;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=immersed boundary method&option=203" rel="nofollow">immersed boundary method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=lattice Boltzmann method&option=203" rel="nofollow">lattice Boltzmann method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=multiblock approach&option=203" rel="nofollow">multiblock approach;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=temperature jump&option=203" rel="nofollow">temperature jump;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=velocity slip&option=203" rel="nofollow">velocity slip;</a> </p> <div class="translation"> 机译：双人口方法;浸没边界法;格子Boltzmann方法;多块方法;温度跳;速度滑; 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href="/journal-cn-7530/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 哈尔滨工程大学学报 </a> </span> <span> . 2006</span><span>,第002期</span> </span> </div> </li> <li> <div> <b>6. </b><a class="enjiyixqcontent" href="/academic-conference-cn_meeting-37459_thesis/020221590326.html">不对称热边界交变流缝隙换热的数值分析和实验研究</a> <b>[C]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=朱绍伟&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 朱绍伟</a> <span> <a href="/conference-cn-37459/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 中国工程热物理学会传热传质学术会 </a> <span> <span> . 1987</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020313541365.html">考虑边界滑移的纯滑动热弹流问题的数值分析</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=陈宏耀&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 陈宏耀</a> <span> . 2018</span> 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