Update the PDE solver tests README file.

Author: Damian Rouson

src/tests/integration/pde_solvers/README.txt

@@ -1,47 +1,47 @@
-This directory contains three one-dimensional partial differential equation
-(PDE) solvers that exercise the parallel programming features of Fortran
-2008: coarrays and "do concurrent".  The solvers are in the following three
-directories:
-
-   (1) coarrayHeatSimplified
-   (2) coarrayBurgers
-   (3) coarrayBurgersStaticTau
-
-The first second and third directories above depend on files in the include-files
-and library directories.
-
-The heat equation solver (1) is the most stringent in terms of correctness
-because it checks for the exact solution at every point across the problem
-domain.  I suggest starting with the heat equation solver to check compiler
-correctness before moving to the other solvers.
-
-The raw Burgers equation solver (2) is slightly more complicated than the
-heat equation solver in that the Burgers solver adds one additional term
-(a nonlinear term), the calculation of which imposes an additional
-synchronization requirement.  However, the correctness test in the Burgers
-equation solver is weak: it checks only one value in the problem domain and
-that point is a point that should remain zero for all time.
-
-The instrumented Burgers solver (3) is best for performance studies.  It has
-been instrumented for performance analysis witih the Tuning and Analysis
-Utilities (TAU), which is open-source software available at
-http://tau.uoregon.edu.  Because of a memory leak in the Intel compiler,
-the instrumented solver uses static rather than dynamic memory.  For this
-reason, the code needs to be recompiled for each desired problem size.  See
-coarrayBurgersStaticTau/math_constants.F90 for an important comment regarding
-matching the problem size with the number of images.
-
-The instrumented Burgers solver has been demonstrated to execute with 99%
-parallel efficiency on over 13,000 cores and 87% parallel efficiency on 16,384
+[This document is formatted with GitHub-Flavored Markdown.   ]:#
+[For better viewing, including hyperlinks, read it online at ]:#
+[https://github.com/sourceryinstitute/opencoarrays/edit/master/src/tests/integration/pde_solvers/README.txt]:#
+
+Partial Differential Equation (PDE) Solvers
+===========================================
+
+This directory contains three PDE solvers listed here in order from simplest to most complex:
+
+* A one-dimensional (1D) finite-difference, unsteady [heat equation solver],
+* A 1D finite-difference, unsteady, nonlinear [Burgers equation solver], and
+* A three-dimensional (3D), unsteady, spectral [Navier-Stokes equation solver].
+
+The first two solvers contain correctness checks that result in the printing of the 
+message "Test passed" before terminating a correct execution.  For more details on the 
+heat equation solver please view the [Sourcery Institute] [tutorial videos] online.  
+
+For more details on the Burgers solver, please see Chapter 12 of the textbook 
+[Scientific Sofware Design] or the open-access journal article 
+"[High Performance Design Patterns for Modern Fortran]."  The [coarrayBurgers] 
+subdirectory includes a [run.sh] launch script that works inside the open-source 
+Linux virtual machine available in the Sourcery Institute [store].
+
+The launch script instruments the Burgers solver for performance analysis using the 
+open-source Tuning and Analysis Utilities ([TAU]) package.  The instrumented Burgers 
+solver has been demonstrated to execute with 87% parallel efficiency on 16,384
 cores in weak scaling when compiled with the Cray Compiler Environment.  For
 new scalabiliby studies, it is important to run problems of sufficient size.
-See one of the following two publications for additional information:
-
-[1] Haveraaen, M., K. Morris, D. W. I. Rouson, H. Radhakrishnan, and C. Carson
-(2014) “High- performance design patterns for modern Fortran,” Scientific
-Programming, in review.
 
-[2] Haveraaen, M., K. Morris, and D. W. I. Rouson (2013) “High-performance design
-patterns for modern Fortran,” First International Workshop on Software
-Engineering for High Performance Computing in Computational Science and
-Engineering, Denver, Colorado, USA. November 22.
+The Navier-Stokes solver uses Fourier-spectral methods and Runge-Kutta time advancement
+to simulate the evolution of statistically homogeneous turbulent flow in a 3D box with 
+periodic boundary conditions.  For performance and complexity comparisons, the 
+[navier-stokes] subdirectory contains both a  Message Passing Interface (MPI) version 
+and a coarray Fortran (CAF) version of the same solution algorithm.
+
+[heat equation solver]: ./coarrayHeatSimplified
+[Burgers equation solver]: ./coarrayBurgers
+[Navier-Stokes equation solver]: ./navier-stokes
+[Sourcery Institute]: http://www.sourceryinstitute.org
+[tutorial videos]: http://www.sourceryinstitute.org/videos
+[Scientific Sofwtware Design]: http://www.cambridge.org/rouson
+[High Performance Design Patterns for Modern Fortran]: http://www.hindawi.com/journals/sp/2015/942059/
+[store]: http://www.sourceryinstitute.org/store
+[coarrayBurgers]: ./coarrayBurgers
+[run.sh]: ./coarrayBurgers/run.sh
+[TAU]: http://tau.uoregon.edu
+[navier-stokes]: ./navier-stokes