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The a(4) Scheme-A High Order Neutrally Stable CESE SolverThe CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3
Document ID
Document Type
Technical Memorandum (TM)
Chang, Sin-Chung
(NASA Glenn Research Center Cleveland, OH, United States)
Date Acquired
August 24, 2013
Publication Date
July 1, 2009
Subject Category
Numerical Analysis
Report/Patent Number
AIAA Paper 2007-5820
Meeting Information
Meeting: 43rd Joint Propulsion Conference
Location: Cincinnati, OH
Country: United States
Start Date: July 8, 2007
End Date: July 11, 2007
Sponsors: American Inst. of Aeronautics and Astronautics
Funding Number(s)
WBS: WBS 599489.
Distribution Limits
Work of the US Gov. Public Use Permitted.
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