欧拉方程最优控制的松弛方法

IF 2.5 3区数学 Q1 MATHEMATICS, APPLIED

Computational & Applied Mathematics Pub Date : 2011-07-18 DOI:10.1590/S1807-03022011000200009

J. T. Ngnotchouye, M. Herty, S. Steffensen, M. Banda

{"title":"欧拉方程最优控制的松弛方法","authors":"J. T. Ngnotchouye, M. Herty, S. Steffensen, M. Banda","doi":"10.1590/S1807-03022011000200009","DOIUrl":null,"url":null,"abstract":"The treatment of control problems governed by systems of conservation laws poses serious challenges for analysis and numerical simulations. This is due mainly to shock waves that occur in the solution of nonlinear systems of conservation laws. In this article, the problem of the control of Euler flows in gas dynamics is considered. Numerically, two semi-linear approximations of the Euler equations are compared for the purpose of a gradient-based algorithm for optimization. One is the Lattice-Boltzmann method in one spatial dimension and five velocities (D1Q5 model) and the other is the relaxation method. An adjoint method is used. Good results are obtained even in the case where the solution contains discontinuities such as shock waves or contact discontinuities.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2011-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"Relaxation approaches to the optimal control of the Euler equations\",\"authors\":\"J. T. Ngnotchouye, M. Herty, S. Steffensen, M. Banda\",\"doi\":\"10.1590/S1807-03022011000200009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The treatment of control problems governed by systems of conservation laws poses serious challenges for analysis and numerical simulations. This is due mainly to shock waves that occur in the solution of nonlinear systems of conservation laws. In this article, the problem of the control of Euler flows in gas dynamics is considered. Numerically, two semi-linear approximations of the Euler equations are compared for the purpose of a gradient-based algorithm for optimization. One is the Lattice-Boltzmann method in one spatial dimension and five velocities (D1Q5 model) and the other is the relaxation method. An adjoint method is used. Good results are obtained even in the case where the solution contains discontinuities such as shock waves or contact discontinuities.\",\"PeriodicalId\":50649,\"journal\":{\"name\":\"Computational & Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2011-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational & Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1590/S1807-03022011000200009\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational & Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1590/S1807-03022011000200009","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 15

摘要

处理由守恒定律系统支配的控制问题对分析和数值模拟提出了严峻的挑战。这主要是由于发生在具有守恒律的非线性系统解中的激波。本文研究了气体动力学中欧拉流的控制问题。数值上，对欧拉方程的两种半线性近似进行了比较，以实现基于梯度的优化算法。一种是一维五速格点-玻尔兹曼方法(D1Q5模型)，另一种是松弛法。采用伴随法。即使溶液中含有不连续面，如激波或接触不连续面，也能获得良好的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Relaxation approaches to the optimal control of the Euler equations

The treatment of control problems governed by systems of conservation laws poses serious challenges for analysis and numerical simulations. This is due mainly to shock waves that occur in the solution of nonlinear systems of conservation laws. In this article, the problem of the control of Euler flows in gas dynamics is considered. Numerically, two semi-linear approximations of the Euler equations are compared for the purpose of a gradient-based algorithm for optimization. One is the Lattice-Boltzmann method in one spatial dimension and five velocities (D1Q5 model) and the other is the relaxation method. An adjoint method is used. Good results are obtained even in the case where the solution contains discontinuities such as shock waves or contact discontinuities.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Computational & Applied Mathematics Mathematics-Computational Mathematics

CiteScore

4.50

自引率

11.50%

发文量

352

审稿时长

>12 weeks

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.