NASA LogoNTRSNTRS - NASA Technical Reports ServerSearchmore_vertCollectionsAboutNewsHelpLogin Back to ResultsAn Application of the Difference Potentials Method to Solving External Problems in CFDNumerical solution of infinite-domain boundary-value problems requires some special techniques that would make the problem available for treatment on the computer. Indeed, the problem must be discretized in a way that the computer operates with only finite amount of information. Therefore, the original infinite-domain formulation must be altered and/or augmented so that on one hand the solution is not changed (or changed slightly) and on the other hand the finite discrete formulation becomes available. One widely used approach to constructing such discretizations consists of truncating the unbounded original domain and then setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The role of the ABC's is to close the truncated problem and at the same time to ensure that the solution found inside the finite computational domain would be maximally close to (in the ideal case, exactly the same as) the corresponding fragment of the original infinite-domain solution. Let us emphasize that the proper treatment of artificial boundaries may have a profound impact on the overall quality and performance of numerical algorithms. The latter statement is corroborated by the numerous computational experiments and especially concerns the area of CFD, in which external problems present a wide class of practically important formulations. In this paper, we review some work that has been done over the recent years on constructing highly accurate nonlocal ABC's for calculation of compressible external flows. The approach is based on implementation of the generalized potentials and pseudodifferential boundary projection operators analogous to those proposed first by Calderon. The difference potentials method (DPM) by Ryaben'kii is used for the effective computation of the generalized potentials and projections. The resulting ABC's clearly outperform the existing methods from the standpoints of accuracy and robustness, in many cases noticeably speed up the multigrid convergence, and at the same time are quite comparable to other methods from the standpoints of geometric universality and simplicity of implementation.Document ID19970017370Acquisition SourceLangley Research CenterDocument TypeTechnical Memorandum (TM)AuthorsRyaben 'Kii, Victor S.*(Academy of Sciences (USSR) Moscow,  USSR)*Tsynkov, Semyon V.*(NASA Langley Research Center Hampton, VA United States)*Date AcquiredSeptember 6, 2013Publication DateMarch 1, 1997Subject CategoryAerodynamicsReport/Patent NumberNAS 1.15:110338NASA-TM-110338Accession Number97N19659Funding Number(s)PROJECT: RTOP 522-31-21-04Distribution LimitsPublicCopyrightWork of the US Gov. Public Use Permitted.Available DownloadsNameType19970017370.pdfSTIcloud_downloadcontent_copyvisibilityRelated RecordsThere are no records associated with this record.visibility_offNo Preview Available
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