The discrete duality finite volume method for a class of quasi‐Newtonian Stokes flows

机译：一类拟牛顿斯托克斯流的离散二元性有限体积法

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Abstract > In this paper, we propose a discrete duality finite volume (DDFV) scheme for the incompressible quasi‐Newtonian Stokes equation. The DDFV method is based on the use of discrete differential operators which satisfy some duality properties analogous to their continuous counterparts in a discrete sense. The DDFV method has a great ability to handle general geometries and meshes. In addition, every component of the velocity gradient can be reconstructed directly, which makes it suitable to deal with the nonlinear terms in the quasi‐Newtonian Stokes equation. We prove that the proposed DDFV scheme is uniquely solvable and of first‐order convergence in the discrete L 2 ‐norms for the velocity, the strain rate tensor, and the pressure, respectively. Ample numerical tests are provided to highlight the performance of the proposed DDFV scheme and to validate the theoretical error analysis, in particular on locally refined nonconforming and polygonal meshes. </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”> <标题类型=“main”>抽象</ title> > 本文提出了一种用于不可压缩的准牛顿斯托克斯方程的离散二元性有限体积（DDFV）方案。 DDFV方法基于使用离散差分运算符，该算子以离散的意义为基础的分歧算子，该算子满足与其连续对应物的一些二元性质。 DDFV方法具有能够处理一般几何形状和网格的能力。另外，可以直接重建速度梯度的每个组件，这使得适合处理Quasi-Newtonian Stokes方程中的非线性术语。我们证明，所提出的DDFV方案是独特的可解下的，并且在离散的情况下是一阶收敛 l </ i> 2 </ sup> - 分别为速度，应变速率张量和压力。提供充足的数值测试以突出所提出的DDFV方案的性能并验证理论误差分析，特别是在局部精制的不合格和多边形网上。 </ 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-26113/'>《Numerical Methods for Partial Differential Equations: An International Journal》</a> <b style="margin: 0 2px;">|</b><span>2019年第6期</span><b style="margin: 0 2px;">|</b><span>共28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=He Zhengkang&option=202" target="_blank" rel="nofollow">He Zhengkang;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Li Rui&option=202" target="_blank" rel="nofollow">Li Rui;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Chen Jie&option=202" target="_blank" rel="nofollow">Chen Jie;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Chen Zhangxin&option=202" target="_blank" rel="nofollow">Chen Zhangxin;</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>School of Mathematics and StatisticsXi'an Jiaotong UniversityXi'an China;</p> <p>School of Mathematics and Information ScienceShaanxi Normal UniversityXi'an China;</p> <p>School of Mathematics and StatisticsXi'an Jiaotong UniversityXi'an China;</p> <p>School of Mathematics and StatisticsXi'an Jiaotong UniversityXi'an China;</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/4646.html" title="数值分析">数值分析;</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=discrete duality finite volume method&option=203" rel="nofollow">discrete duality finite volume method;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=distorted&option=203" rel="nofollow">distorted;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=nonconforming and polygonal meshes&option=203" rel="nofollow">nonconforming and polygonal meshes;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=quasi‐Newtonian Stokes equation&option=203" rel="nofollow">quasi‐Newtonian Stokes equation;</a> </p> <div class="translation"> 机译：离散的二元性有限体积法;扭曲;不合格和多边形网格;准牛顿斯托克斯方程式; 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