
Accession Number : AD0849487
Title : The Convergence of Numerical Solutions of Hydrodynamic Shock Problems.
Descriptive Note : Technical rept. May 68Jan 69,
Corporate Author : AIR FORCE WEAPONS LAB KIRTLAND AFB NM
Personal Author(s) : Hicks, Darrell Lee
Report Date : MAR 1969
Pagination or Media Count : 121
Abstract : In 1944 von Neumann conjectured that only the averages of numerical solutions, produced by a discrete scheme he had proposed to solve hydrodynamic shock problems, would converge as the meshes were refined. The hydrodynamic shock problem is defined here as follows: find a solution, allowing discontinuous solutions, to the three conservation laws, the increasingentropy law, and the idealgas law when given physically acceptable initial and boundary values. For discrete schemes similar to von Neumann's, it is verified that the averages do converge and it appears that von Neumann was also correct in surmising that only the averages converge. A smoothing device named 'conservative smoothing' is developed and has been successfully introduced into one, two, and threedimension hydrocodes. A conservative discrete scheme with conservative smoothing, in the onedimension Lagrangian formulation, produces in the limit, for a suitably chosen sequence of meshes, generalized functions which satisfy the conservation laws. A priori bounds and convergence and compactness lemmas for sequences of solution refinements in LPspaces are developed. (Author)
Descriptors : *NUMERICAL ANALYSIS), (*HYDRODYNAMICS, SHOCK(MECHANICS), CONVERGENCE, BOUNDARY VALUE PROBLEMS, BOUNDARY VALUE PROBLEMS, INEQUALITIES, THEOREMS, ENTROPY.
Subject Categories : Theoretical Mathematics
Fluid Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE