New family of adaptive very high resolution schemes

The family of skew very high resolution (VHR) schemes is adaptively combined with the family of high-resolution (HR) schemes to yield a new family of adaptive very high resolution (AVHR) schemes. A new simple adaptive switching criterion is devised. For convection-diffusion type problems the adaptive schemes are accelerated by using in tandem the normalized weighting factor method to implement the HR scheme and the deferred-correction (DC) procedure to implement the skew scheme. For flow problems the DC procedure is used to implement both types of schemes. Numerical results for the new family of AVHR schemes are compared in terms of accuracy and computation cost against those generated using the VHR base family of schemes by solving four problems: (I) pure convection of a step profile in an oblique velocity field, (2) driven flow in a skew cavity, (3) laminar sudden expansion of an oblique velocity field in a rectangular cavity, (4) and turbulent sudden expansion of an oblique velocity field in a rectangular cavity

[1]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[2]  M. Darwish,et al.  NEW BOUNDED SKEW CENTRAL DIFFERENCE SCHEME, PART I: FORMULATION AND TESTING , 1997 .

[3]  M. Darwish,et al.  The normalized weighting factor method : A novel technique for accelerating the convergence of high-resolution convective schemes , 1996 .

[4]  S. Osher,et al.  High resolution applications of the Osher upwind scheme for the Euler equations , 1983 .

[5]  M. Peric.  A finite volume method for the prediction of three-dimensional fluid flow in complex ducts , 1985 .

[6]  Yih Nen Jeng,et al.  An Adaptive TVD Limiter , 1995 .

[7]  B. P. Leonard,et al.  Beyond first‐order upwinding: The ultra‐sharp alternative for non‐oscillatory steady‐state simulation of convection , 1990 .

[8]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme , 1974 .

[9]  P. Gaskell,et al.  Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm , 1988 .

[10]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[11]  M. Darwish,et al.  AN EFFICIENT VERY-HIGH-RESOLUTION SCHEME BASED ON AN ADAPTIVE-SCHEME STRATEGY , 1998 .

[12]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[13]  Sumanta Acharya,et al.  AN ADAPTIVE DIFFERENCING SCHEME FOR FLOW AND HEAT TRANSFER PROBLEMS , 1993 .

[14]  M. Darwish,et al.  A NEW HIGH-RESOLUTION SCHEME BASED ON THE NORMALIZED VARIABLE FORMULATION , 1993 .

[15]  M. Darwish,et al.  NORMALIZED VARIABLE AND SPACE FORMULATION METHODOLOGY FOR HIGH-RESOLUTION SCHEMES , 1994 .

[16]  M. Darwish,et al.  A NEW FAMILY OF STREAMLINE-BASED VERY-HIGH-RESOLUTION SCHEMES , 1997 .

[17]  B. P. Leonard,et al.  The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection , 1991 .