A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock‐capturing on cut cells

Geisenhofer Markus; Kummer Florian; Müller Bj?rn

摘要

Summary >We present a higher‐order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity–based shock‐capturing approach. The cut cell grid is optimized by a nonintrusive cell agglomeration strategy in order to avoid problems with small or ill‐shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero isocontour of a level set function. In flow configurations with high Mach numbers, a numerical shock‐capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second‐order diffusive term and small nonagglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach are verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries. </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 =“FLD4761-ABS-ABS-0001”> <标题类型=“main”>摘要</ title> >我们提出了一种高阶切割的细胞浸没边界法（IBM），用于仿真高马赫数流。作为剪切电池网格上的新颖性，我们评估了一种与人工粘度的冲击捕获方法的适应局部时间踩踏（LTS）方案。切割电池网格通过非耐纤维聚集策略优化，以避免小或不形状的切割细胞的问题。我们的方法基于可压缩欧拉方程的不连续的Galerkin离散化，其中浸没边界由级别集功能的零Isocontour隐含地定义。在具有高马赫数的流动配置中，数值冲击捕获机构是至关重要的，以防止在冲击附近的多项式近似的不经密地振荡。我们通过粘性平滑实现这一点，其中人工粘度从已经适应于IBM的模态衰减传感器。通过使用自适应LTS算法来解决由额外的二阶扩散术语和小非聚集切割细胞引起的严重时间步长的问题。我们方法的鲁棒性，稳定性和准确性验证了几个常见的测试用例。此外，结果表明，我们的方法急剧降低了计算成本，特别是对于具有复杂几何形状的不稳定IBM问题。</ 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9期</span><b style="margin: 0 2px;">|</b><span>共25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=Geisenhofer Markus&option=202" target="_blank" rel="nofollow">Geisenhofer Markus;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Kummer Florian&option=202" target="_blank" rel="nofollow">Kummer Florian;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Müller Bj?rn&option=202" target="_blank" rel="nofollow">Müller Bj?rn;</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>Chair of Fluid DynamicsTechnische Universit?t DarmstadtDarmstadt Germany;</p> <p>Chair of Fluid DynamicsTechnische Universit?t DarmstadtDarmstadt Germany;</p> <p>Chair of Fluid DynamicsTechnische Universit?t DarmstadtDarmstadt 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=compressible flow&option=203" rel="nofollow">compressible flow;</a> <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=immersed boundary&option=203" rel="nofollow">immersed boundary;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=level set&option=203" rel="nofollow">level set;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=supersonic&option=203" rel="nofollow">supersonic;</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> </p> <div class="translation"> 机译：可压缩流动;不连续的Galerkin;浸没边界;水平设定;超音速;时间集成; </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 >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704022975832.html">A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock‐capturing on cut cells</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Geisenhofer Markus&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Geisenhofer Markus,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Kummer Florian&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Kummer Florian,</a> <a 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