국내 최대 기계 및 로봇 연구정보

기술보고서

기술보고서 게시판 내용
타이틀	Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions
저자	Fisher, Travis C.;; Carpenter, Mark H.;; Nordstroem, Jan;; Yamaleev, Nail K.;; Swanson, R. Charles
Keyword	BOUNDARY CONDITIONS;; CONSERVATION LAWS;; DISCRETIZATION (MATHEMATICS); ERRORS;; EULER EQUATIONS OF MOTION;; FINITE DIFFERENCE THEORY;; NONLINEARITY;; NUMERICAL STABILITY;; OPERATORS (MATHEMATICS); SIMULATION
URL	http://hdl.handle.net/2060/20110023654
보고서번호	NASA/TM-2011-217307
발행년도	2011
출처	NTRS (NASA Technical Report Server)
ABSTRACT	Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived;; these guarantee the conservative form of the combined operator.