Multistep lattice Boltzmann methods: Theory and applications

Wilde Dominik; Kr?mer Andreas; Küllmer Knut; Foysi Holger; Reith Dirk

摘要

Summary >This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second‐order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third‐order accurate Adams‐Moulton method and the second‐order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier. </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 Type =“Main”XML：Lang =“EN”XML：ID =“FLD4716-ABS-0001”> <标题类型=“main”>摘要</ title> >本文介绍了一种用于将任意隐式多步骤的方案纳入晶格Boltzmann方法的框架。虽然晶格Boltzmann方程的时间离散化通常使用二阶梯形规则导出，但是通过使用多步骤方法来增强时间离散化来似乎自然。在准确性和稳定性方面研究将MultiSep方法掺入晶格Boltzmann方法中的效果。三阶准确的Adams-Moulton方法和二阶向下分化公式的数值测试表明，当根据第二个Dahlquist屏障考虑多步骤方法的稳定性特性时，可以增加该方法的时间顺序。</ 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>2019年第3期</span><b style="margin: 0 2px;">|</b><span>共14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=Wilde Dominik&option=202" target="_blank" rel="nofollow">Wilde Dominik;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Kr?mer Andreas&option=202" target="_blank" rel="nofollow">Kr?mer Andreas;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Küllmer Knut&option=202" target="_blank" rel="nofollow">Küllmer Knut;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Foysi Holger&option=202" target="_blank" rel="nofollow">Foysi Holger;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Reith Dirk&option=202" target="_blank" rel="nofollow">Reith Dirk;</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>Institute for Technology Renewables and Energy‐efficient Engineering (TREE)Bonn‐Rhein‐Sieg University of Applied SciencesSankt Augustin Germany;</p> <p>Institute for Technology Renewables and Energy‐efficient Engineering (TREE)Bonn‐Rhein‐Sieg University of Applied SciencesSankt Augustin Germany;</p> <p>Institute for Technology Renewables and Energy‐efficient Engineering (TREE)Bonn‐Rhein‐Sieg University of Applied SciencesSankt Augustin Germany;</p> <p>Department of Mechanical EngineeringUniversity of SiegenSiegen Germany;</p> <p>Institute for Technology Renewables and Energy‐efficient Engineering (TREE)Bonn‐Rhein‐Sieg University of Applied SciencesSankt Augustin Germany;</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=Adams‐Moulton&option=203" rel="nofollow">Adams‐Moulton;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=BDF&option=203" rel="nofollow">BDF;</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=multistep&option=203" rel="nofollow">multistep;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=stability&option=203" rel="nofollow">stability;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Taylor‐Green&option=203" rel="nofollow">Taylor‐Green;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=temporal discretization&option=203" rel="nofollow">temporal discretization;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=time integration&option=203" rel="nofollow">time integration;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=trapezoidal rule&option=203" rel="nofollow">trapezoidal rule;</a> </p> <div class="translation"> 机译：Adams-Moulton;BDF;格子Boltzmann方法;多步;稳定性;泰勒 - 绿色;时间离散化;时间集成;时间集成;梯形规则; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704022976155.html">Multistep lattice Boltzmann methods: Theory and applications</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wilde Dominik&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Wilde Dominik,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Kr?mer Andreas&option=202" target="_blank" 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href="/patent-detail/061204058743.html">一种基于Lattice LSTM和语言模型的命名实体识别方法</a> <b>[P]</b> . <span> 中国专利： CN109284400B </span> <span> . 2020.10.23</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120103559868.html">基于Lattice编码放大转发的网络编码方法及系统</a> <b>[P]</b> . <span> 中国专利： CN110971286A </span> <span> . 2020-04-07</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130414182000.html">METHOD FOR SIMULATING FLUID FLOW BY USING THE LATTICE BOLTZMANN THEORY AND RECORDING MEDIUM FOR PERFORMING THE METHOD</a> <b>[P]</b> . <span> 外国专利：  KR20150091592A </span> <span> . 2015-08-12</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：利用格子Boltzmann理论和记录介质来模拟流体流动的方法 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130414063942.html">Method for simulating fluid 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