New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

Conference · Tue Jun 01 04:00:00 EDT 1993

OSTI ID:5863655

Chang, Sinchung

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

• Research Organization: National Aeronautics and Space Administration, Cleveland, OH (United States). Lewis Research Center
• OSTI ID: 5863655
• Report Number(s): N-94-10939; NASA-TM--106226; E--7943; NAS--1.15:106226; CONF-930889--; CNN: RTOP 505-62-52
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
CALCULATION METHODS
CONSERVATION LAWS
CONVECTION
DIFFERENTIAL EQUATIONS
DIFFUSION
ENERGY TRANSFER
EQUATIONS
HEAT TRANSFER
MASS TRANSFER
NAVIER-STOKES EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SHOCK TUBES