Matrix‐free modified extended BDF applied to the discontinuous Galerkin solution of unsteady compressible viscous flows

Nigro A.; De Bartolo C.; Crivellini A.; Bassi F.

摘要

Summary >In this work, a time‐accurate integration of the discontinuous Galerkin space‐discretized Navier‐Stokes equations is performed exploiting the matrix‐free (MF) approach to speed up the solution process of the modified extended backward differentiation formulae (MEBDF) schemes. MEBDF are high‐order accurate implicit multistep schemes composed by three nonlinear stages. The proposed algorithm consists in solving the resulting nonlinear system of each stage with a preconditioned MF Newton/Krylov method using a frozen preconditioner strategy to improve its efficiency. Numerical results for compressible inviscid and viscous test cases, both with a known analytical solution, aim at assessing the performance of the proposed MF‐MEBDF algorithm, by comparing it with the one obtained by using its matrix‐explicit counterpart or the explicit strong stability preserving Runge‐Kutta scheme. In particular, the influence of some relevant physical (low‐speed flows) and discretization (aspect ratio, polynomial degree) aspects on the performance of the different time integration schemes are investigated, highlighting the pros and cons of the proposed algorithm and its effectiveness in solving nonstiff and stiff systems. Furthermore, the scalability in parallel computations of the proposed algorithm is investigated and, finally, its potential for efficient long‐time simulations is demonstrated computing a laminar vortex shedding behind a circular cylinder at different Reynolds numbers and by comparing its effectiveness with that of the strong stability preserving Runge‐Kutta scheme. </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：lang =“en”xml：id =“fld4679-abs-abs-0001”> <标题类型=“main”>摘要</ title> 在这项工作中，执行不连续Galerkin空间离散的Navier-Stokes方程的时间准确集成利用矩阵（MF）方法来加速修改的延伸后向区分式（MEBDF）的解决方案过程方案。 MEBDF是由三个非线性阶段组成的高阶准确的隐式多步模板。所提出的算法包括使用冷冻预处理器策略来解决每个阶段的所得非线性系统，使用冻结的预处理器策略来提高其效率。可压缩反应和粘性测试用例的数值结果，既通过已知的分析解决方案，目的在评估所提出的MF-MEBDF算法的性能，通过将其与通过使用其矩阵显式对应物或明确的强稳定性保留而获得的算法进行比较Runge-Kutta方案。特别地，研究了一些相关物理（低速流动）和离散化（纵横比，多项式）方面对不同时间集成方案的性能的影响，突出了所提出的算法的优缺点及其效果解决非抗控和僵硬的系统。此外，研究了所提出的算法的并行计算中的可扩展性，最后，其对有效的长时间模拟的电位计算在不同的雷诺数的圆筒后面的圆筒后面计算层状涡流，并通过比较强大的效果稳定性保存runge-kutta方案。</ 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12期</span><b style="margin: 0 2px;">|</b><span>共29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=Nigro A.&option=202" target="_blank" rel="nofollow">Nigro A.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=De Bartolo C.&option=202" target="_blank" rel="nofollow">De Bartolo C.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Crivellini A.&option=202" target="_blank" rel="nofollow">Crivellini A.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Bassi F.&option=202" target="_blank" rel="nofollow">Bassi F.;</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>University of Calabria Department of MechanicalEnergy and Management Engineering‐DIMEGRende Calabria Italy;</p> <p>University of Calabria Department of MechanicalEnergy and Management Engineering‐DIMEGRende Calabria Italy;</p> <p>Polytechnic University of MarcheDepartment of Industrial Engineering and Mathematical SciencesAncona Marche Italy;</p> <p>University of BergamoDepartment of EngineeringDalmine Bergamo Italy;</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=discontinuous Galerkin&option=203" rel="nofollow">discontinuous Galerkin;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=frozen preconditioner strategy&option=203" rel="nofollow">frozen preconditioner strategy;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=matrix‐free approximation&option=203" rel="nofollow">matrix‐free approximation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=modified extended backward differentiation formulae&option=203" rel="nofollow">modified extended backward differentiation formulae;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=stiff and nonstiff system of equations&option=203" rel="nofollow">stiff and nonstiff system of equations;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=unsteady flows&option=203" rel="nofollow">unsteady flows;</a> </p> <div class="translation"> 机译：不连续的Galerkin;冷冻预处理器策略;无矩阵近似;改进的延伸后向差分公式;刚性和非谐波系统的方程式;不稳定的流动; 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