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Te* OCT 12 1982 



SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) 



REPORT DOCUMENTATION PAGE 



READ INSTRUCTIONS 

 BEFORE COMPLETING FORM 



I. REPORT NUMBER 



DTNSRDC-82/077 



2. GOVT ACCESSION NO 



3. RECIPIENT'S CATALOG NUMBER 



4. TITLE (and Subtitle) 



A VARIATIONAL PRINCIPLE ASSOCIATED WITH A 



LOCALIZED NUMERICAL SOLUTION OF UNSTEADY 



FREE-SURFACE FLOWS 



5. TYPE OF REPORT a PERIOD COVERED 



Final 



6. PERFORMING ORG. REPORT NUMBER 



7. AUTHORfsj 



B. Yim 



B. CONTRACT OR GRANT NUMBERfsJ 



9. PERFORMING ORGANIZATION NAME AND ADDRESS 



David W. Taylor Naval Ship Research 

 and Development Center 

 Bethesda, Maryland 20084 



10. PROGRAM ELEMENT. PROJECT, TASK 

 AREA d WORK UNIT NUMBERS 



Program Element 61153N 

 Task Area RR0140302 

 Work Unit 1542-018 



11. CONTROLLING OFFICE NAME AND ADDRESS 



Office of Naval Research (ONR-432) 

 Arlington, Virginia 



12. REPORT DATE 



September 1982 



13. NUMBER OF PAGES 

 22 



U MONITORING AGENCY NAME ft ADDRESSf// dllterent from Control I Intf Olllce) 



15 SECURITY CLASS, (ol this report) 



UNCLASSIFIED 



16. DISTRIBUTION STATEMENT (ol this Report) 



APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED 



17. DISTRIBUTION STATEMENT (ol the abstract entered In Block 20, II dllterent trom Report) 



18. SUPPLEMENTARY NOTES 



19. KEY WORDS (Contln 



Variational Principle 

 Finite Element Technique 

 Free Surface 

 Functional 



ssary and Identity by block number) 



Numerical Ship Hydrodynamics 

 Nonlinear Theory 

 Convolution 



ABSTRACT (Continue on reverse side If necessary and Identity by block number) 



In this report, a variational principle for unsteady body wave problems 

 is treated both with and without a convolution integral and with both linear 

 and nonlinear free-surface conditions. Functionals are obtained for the 

 numerical computation of unsteady flow fields near a body that moves on or 

 beneath the free surface. This formulation can be applied to ship hydro- 

 dynamic performance problems of water entry and body slamming, as well as to 

 arbitrary body motion. 



DD 



EDITION OF 1 NOV 65 IS OBSOLETE 



S/N 0102-LF-014-6601 



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