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Introduction to Physics and Numerics of NAS Benchmarks

This is first of three foilsets on CFD and NAS Benchmarks

This describes the four basic NAS benchmarks and their relation to the Navier Stokes Equations in the the 5 component CFD equations

We use opportunity to discuss time discretization and stepping in general based on Hirsch CFD book and Numerical Recipes

Stability, Implicit and Explicit formulations are introduced

Beam Warming Equations and their stability

Table of Contents for Introduction to Physics and Numerics of NAS Benchmarks

001 CPS713 Case Study II) CFD and Numerical Relativity
    NAS Part I -- Initial NAS Benchmark Setup
002 Abstract of CPS713-Case Study II 
    Initial NAS Benchmark Setup
003 NAS Parallel Benchmarks 
004 Summary of Sec 3: NAS Parallel Benchmarks:The CFD Kernels
005 Overview of Four Computational (PDE Solver) Kernels in
    NAS Parallel Benchmarks
006 First Two Computational Kernels
007 Second Two Computational Kernels
008 The First Two Simplifications of the NAS Parallel Benchmarks
009 The Second Two Simplifications of the NAS Parallel Benchmarks
010 Basic Formalism for 5 Component CFD
011 What is relation of NAS benchmarks to Navier Stokes Equations -- 
    Terms E F G?
012 What is relation of NAS benchmarks to Navier Stokes Equations -- 
    Terms  T V W ?
013 What is relation of NAS benchmarks to Navier Stokes Equations-- 
    Term H and Boundary Conditions ?
014 What is relation of NAS benchmarks to Navier Stokes Equations -- 
    Space and Time Variables
015 Treatment of Time Discretization for PDE's
016 Treatment of Time Stepping for PDE's :
    Numerical Recipes -- Chapter 19
017 Comparison of Different Methods for Solving Linear Convection 
    Equation
018 Overview of Stability and Accuracy of Partial Differential 
    Equation Solvers
019 Solution of Homogenous Equations by Fourier Analysis
020 Solution of Linear Stability Equations for the Linear Convection 
    Equation
021 General Stability Analysis of some two-step Methods -- Basic 
    Iteration Equation
022 Differential Operator and its Eigenvalues for Beam Warming 
    Equations
023 Stability Conditions for Beam Warming Equations 
024 The effect of Nonlinearity on Implicit Equations

Northeast Parallel Architectures Center, Syracuse University, npac@npac.syr.edu