An adaptive multilevel wavelet framework for scale‐selective WENO reconstruction schemes

Maulik R.; San O.; Behera R.

摘要

Summary >We put forth a dynamic computing framework for scale‐selective adaptation of weighted essential nonoscillatory (WENO) schemes for the simulation of hyperbolic conservation laws exhibiting strong discontinuities. A multilevel wavelet‐based multiresolution procedure, embedded in a conservative finite volume formulation, is used for a twofold purpose. (i) a dynamic grid adaptation of the solution field for redistributing grid points optimally (in some sense) according to the underlying flow structures, and (ii) a dynamic minimization of the in built artificial dissipation of WENO schemes. Taking advantage of the structure detection properties of this multiresolution algorithm, the nonlinear weights of the conventional WENO implementation are selectively modified to ensure lower dissipation in smoother areas. This modification is implemented through a linear transition from the fifth‐order upwind stencil at the coarsest regions of the adaptive grid to a fully nonlinear fifth‐order WENO scheme at areas of high irregularity. Therefore, our computing algorithm consists of a dynamic grid adaptation strategy, a scale‐selective state reconstruction, a conservative flux calculation, and a total variation diminishing Runge‐Kutta scheme for time advancement. Results are presented for canonical examples drawn from the inviscid Burgers, shallow water, Euler, and magnetohydrodynamic equations. Our findings represent a novel direction for providing a scale‐selective dissipation process without a compromise on shock capturing behavior for conservation laws, which would be a strong contender for dynamic implicit large eddy simulation approaches. </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 =“fld4489-abs-abs-0001”> <标题类型=“main”>摘要</ title> >我们提出了一种动态计算框架，用于对加权基本非张位（WENO）方案的比例选择性调整，用于模拟表现出强大的不连续性的双曲守恒法。嵌入在保守的有限体积配方中的一种基于多级小波的多分辨率步骤用于双重目的。（i）根据底层流动结构，最佳地（在某种意义上）重新分配网格点的动态网格适配，（ii）Weno方案的建造人工耗散的动态最小化。利用该多分辨率算法的结构检测特性，选择性地修改了传统Weno实现的非线性重量，以确保在更平滑的区域下耗散。该修改通过自适应网格的粗型载波模板的线性转换来实现，该方法在高度不规则性的区域处于完全非线性的第五阶Weno方案。因此，我们的计算算法包括动态网格适应策略，比例选择性状态重建，保守助熔剂计算以及用于时间进步的总变化递减速率-Kutta方案。从官方汉堡，浅水，欧拉和磁性信息动力学方程中汲取的规范示例提出了结果。我们的发现代表了一种新颖的方向，用于提供规模选择性耗散过程，而没有妥协的缓冲捕获行为，用于保护法律，这将是动态隐式大涡模拟方法的强大竞争者。</ 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5期</span><b style="margin: 0 2px;">|</b><span>共31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=Maulik R.&option=202" target="_blank" rel="nofollow">Maulik R.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=San O.&option=202" target="_blank" rel="nofollow">San O.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Behera R.&option=202" target="_blank" rel="nofollow">Behera R.;</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 Mechanical and Aerospace EngineeringOklahoma State UniversityOklahoma USA;</p> <p>School of Mechanical and Aerospace EngineeringOklahoma State UniversityOklahoma USA;</p> <p>Department of Mathematics and StatisticsIndian Institute of Science Education and Research KolkataNadia India;</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=adaptive mesh refinement&option=203" rel="nofollow">adaptive mesh refinement;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=compact orthogonal wavelets&option=203" rel="nofollow">compact orthogonal wavelets;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=finite volume framework&option=203" rel="nofollow">finite volume framework;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=multiresolution analysis&option=203" rel="nofollow">multiresolution analysis;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=scale‐selective dissipation&option=203" rel="nofollow">scale‐selective dissipation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=WENO reconstruction&option=203" rel="nofollow">WENO reconstruction;</a> </p> <div class="translation"> 机译：自适应网格细化;紧凑的正交小波;有限体积框架;多分辨率分析;比例选择性耗散;文戈重建; </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 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class="enjiyixqcontent" href="/patent-detail/06120106075147.html">自适应分配多级速率方法和多级速率自适应配置器</a> <b>[P]</b> . <span> 中国专利： CN101867438A </span> <span> . 2010-10-20</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130423350910.html">SYSTEM AND METHOD FOR MULTI-SCALE IMAGE RECONSTRUCTION USING WAVELETS</a> <b>[P]</b> . <span> 外国专利：  US2012014617A1 </span> <span> . 2012-01-19</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：小波用于多尺度图像重建的系统和方法 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130441256990.html">High definition digital image wavelet coded processing scrambling technique having digital word stream modified same format original stream and adaptive/progressive reconstruction following function destination user digital profile</a> <b>[P]</b> . <span> 外国专利：  FR2850515A1 </span> <span> . 2004-07-30</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：高清晰度数字图像小波编码处理加扰技术，其功能是将数字字流修改为相同格式的原始流，并根据功能目标用户数字配置文件进行自适应/渐进式重构 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130420670237.html">Wavelet transform apparatus and method based on prediction-update lifting scheme, and adaptive prediction apparatus and method and recording medium for the same</a> <b>[P]</b> . <span> 外国专利：  US8559509B2 </span> <span> . 2013-10-15</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：基于预测-更新提升方案的小波变换装置和方法，以及自适应预测装置和方法以及用于其的记录介质 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" 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