Dynamic Grid Deformation: Continuous Mapping Approach

Herein, we review our effort to date with the development of a deformable-coordinates multi-scale anelastic model. The model is designed using a synergetic interaction between the rules of continuous mapping and the strengths of nonoscillatory forward-in-time (NFT) numerical schemes. This approach leads to an efficacious computational model that is highly accurate and capable of simulating a wide variety of flows.

[1]  L. Rosenhead.  Theoretical Hydrodynamics , 1960, Nature.

[2]  R. Aris.  Vectors, Tensors and the Basic Equations of Fluid Mechanics , 1962 .

[3]  Joe F. Thompson,et al.  Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies , 1974 .

[4]  Richard C. J. Somerville,et al.  On the use of a coordinate transformation for the solution of the Navier-Stokes equations , 1975 .

[5]  P. Thomas,et al.  Geometric Conservation Law and Its Application to Flow Computations on Moving Grids , 1979 .

[6]  Krzysztof Maurin.  Analysis: Part II Integration, Distributions, Holomorphic Functions, Tensor and Harmonic Analysis , 1980 .

[7]  J. Gregory.  Middle atmosphere dynamics , 1981, Nature.

[8]  R. Hemler,et al.  A Scale Analysis of Deep Moist Convection and Some Related Numerical Calculations , 1982 .

[9]  R. Ogden.  Non-Linear Elastic Deformations , 1984 .

[10]  T. Clark,et al.  Severe Downslope Windstorm Calculations in Two and Three Spatial Dimensions Using Anelastic Interactive Grid Nesting: A Possible Mechanism for Gustiness , 1984 .

[11]  W. R. Peltier,et al.  The Structure and Nonlinear Evolution of Synoptic Scale Cyclones: Life Cycle Simulations with a Cloud-Scale Model , 1990 .

[12]  Piotr K. Smolarkiewicz,et al.  A class of monotone interpolation schemes , 1992 .

[13]  P. Smolarkiewicz,et al.  A class of semi-Lagrangian approximations for fluids. , 1992 .

[14]  P. Smolarkiewicz,et al.  On Forward-in-Time Differencing for Fluids: Extension to a Curvilinear Framework , 1993 .

[15]  R. Garcia,et al.  Propagation and Breaking at High Altitudes of Gravity Waves Excited by Tropospheric Forcing , 1996 .

[16]  L. Margolin,et al.  MPDATA: A Finite-Difference Solver for Geophysical Flows , 1998 .

[17]  D. Durran.  Numerical methods for wave equations in geophysical fluid dynamics , 1999 .

[18]  R. Rotunno,et al.  Vorticity and potential vorticity in mountain wakes , 1999 .

[19]  M. Shashkov,et al.  A discrete operator calculus for finite difference approximations , 2000 .

[20]  P. K. Smolarkiewicz,et al.  VARIATIONAL METHODS FOR ELLIPTIC PROBLEMS IN FLUID MODELS , 2000 .

[21]  Len G. Margolin,et al.  Implicit Turbulence Modeling for High Reynolds Number Flows , 2001 .

[22]  L. Margolin,et al.  A Class of Nonhydrostatic Global Models. , 2001 .

[23]  L. Margolin,et al.  A rationale for implicit turbulence modelling , 2001 .

[24]  P. Smolarkiewicz,et al.  A multiscale anelastic model for meteorological research , 2002 .

[25]  Piotr K. Smolarkiewicz,et al.  FORWARD-IN-TIME DIFFERENCING FOR FLUIDS: SIMULATION OF GEOPHYSICAL TURBULENCE , 2002 .

[26]  J. Prusa,et al.  An all-scale anelastic model for geophysical flows: dynamic grid deformation , 2003 .

[27]  Terry Davies,et al.  Validity of anelastic and other equation sets as inferred from normal‐mode analysis , 2003 .

[28]  Akio Arakawa,et al.  CLOUDS AND CLIMATE: A PROBLEM THAT REFUSES TO DIE. Clouds of many , 2022 .

[29]  P. Smolarkiewicz,et al.  Effective eddy viscosities in implicit large eddy simulations of turbulent flows , 2003 .

[30]  N. Wedi,et al.  Extending Gal-Chen and Somerville terrain-following coordinate transformation on time-dependent curvilinear boundaries , 2004 .

[31]  N. Wedi,et al.  Laboratory for internal gravity‐wave dynamics: the numerical equivalent to the quasi‐biennial oscillation (QBO) analogue , 2005 .

[32]  J. Szmelter,et al.  MPDATA: An edge-based unstructured-grid formulation , 2005 .