William C. Tyson, Charles W. Jackson, Christopher J Roy
{"title":"Development and Verification of a Higher-Order Computational Fluid Dynamics Solver","authors":"William C. Tyson, Charles W. Jackson, Christopher J Roy","doi":"10.1115/1.4064620","DOIUrl":null,"url":null,"abstract":"\n Over the past two decades, higher-order methods have gained much broader use in computational science and engineering as these schemes are often more efficient per degree-of-freedom at achieving a prescribed error tolerance than lower-order methods. During this time, higher-order variants of most discretization schemes, such as finite-difference methods, finite-volume methods, and finite-element methods, have emerged. The finite-volume method is arguably the most widely used discretization technique in production-level computational fluid dynamics solvers due to its robustness and conservation properties. However, most finite-volume solvers only employ a conventional second-order scheme. To leverage the benefits of higher-order methods, the higher-order finite-volume method seems the most natural for those seeking to extend their legacy solvers to higher-order. Nonetheless, ensuring higher-order accuracy is maintained is quite challenging as the implementation requirements for a higher-order scheme are much greater than that of a lower-order scheme. In this work, a methodology for verifying higher-order finite-volume codes is presented. The higher-order finite-volume method is outlined in detail. Order verification tests are proposed for all major components, including the treatment of curved boundaries and the higher-order solution reconstruction. System-level verification tests are performed using the weak form of the Method of Manufactured Solutions. Several canonical verification cases are also presented for the Euler and laminar Navier-Stokes equations.","PeriodicalId":52254,"journal":{"name":"Journal of Verification, Validation and Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Verification, Validation and Uncertainty Quantification","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/1.4064620","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Over the past two decades, higher-order methods have gained much broader use in computational science and engineering as these schemes are often more efficient per degree-of-freedom at achieving a prescribed error tolerance than lower-order methods. During this time, higher-order variants of most discretization schemes, such as finite-difference methods, finite-volume methods, and finite-element methods, have emerged. The finite-volume method is arguably the most widely used discretization technique in production-level computational fluid dynamics solvers due to its robustness and conservation properties. However, most finite-volume solvers only employ a conventional second-order scheme. To leverage the benefits of higher-order methods, the higher-order finite-volume method seems the most natural for those seeking to extend their legacy solvers to higher-order. Nonetheless, ensuring higher-order accuracy is maintained is quite challenging as the implementation requirements for a higher-order scheme are much greater than that of a lower-order scheme. In this work, a methodology for verifying higher-order finite-volume codes is presented. The higher-order finite-volume method is outlined in detail. Order verification tests are proposed for all major components, including the treatment of curved boundaries and the higher-order solution reconstruction. System-level verification tests are performed using the weak form of the Method of Manufactured Solutions. Several canonical verification cases are also presented for the Euler and laminar Navier-Stokes equations.