FLOWFIELD-DEPENDENT MIXED EXPLICIT-IMPLICIT (FDMEI) METHODS FOR HIGH AND LOW-SPEED AND COMPRESSIBLE AND INCOMPRESSIBLE FLOWS

Despite significant achievements in computational fluid dynamics, ther e still remain many fluid flow phenomena not well understood. For exam ple, the prediction of temperature distributions is inaccurate when te mperature gradients are high, particularly in shock wave turbulent bou ndary layer interactions close to the wall. Complexities of fluid flow phenomena include transition to turbulence, relaminarization, separat ed Rows, transition between viscous and inviscid, incompressible and c ompressible flows, among others, in all speed regimes. The purpose of this paper is to introduce a new approach, called the Flowfield-Depend ent Mixed Explicit-Implicit (FDMEI) method, in an attempt to resolve t hese difficult issues in CFD. In this process, a total of six implicit ness parameters characteristic of the current flowfield are introduced . They are calculated from the current flowfield or changes of Mach nu mbers, Reynolds numbers, Peclet numbers, and Damkohler numbers (if rea cting) at each nodal point and time step. This implies that every noda l point or element is provided with different or unique numerical sche me according to their current flowfield situations, whether compressib le, incompressible, viscous, inviscid, laminar, turbulent, reacting, o r nonreacting. In this procedure, discontinuities or fluctuations of a ll variables between adjacent nodal points are determined accurately. If these implicitness parameters are fixed to certain numbers instead of being calculated from the flowfield information, then practically a ll currently available schemes of finite differences or finite element s arise as special cases. Some benchmark problems to be presented in t his paper will show the validity, accuracy, and efficiency of the prop osed methodology.