CleverLeaf is a hydrodynamics mini-app that extends CloverLeaf with Adaptive Mesh Refinement using the SAMRAI toolkit from Lawrence Livermore National Laboratory. The primary goal of CleverLeaf is to evaluate the application of AMR to the Lagrangian-Eulerian hydrodynamics scheme used by CloverLeaf.

Ensure you have SAMRAI (and it's dependencies installed). Edit Make.inc, ensuring that HDF_DIR and BOOST_DIR and SAMRAI_DIR point to the correct locations, and that COMPILER, CXX, and F90 are set appropriately.

To build the reference version, type: make ref

To run the test problem, type: make test
N.B. Running the test assumes that the command mpirun can be used to launch an executable.

To run other problems:

mpirun -n ./cleverleaf <input_file>

Substitute mpirun with the appropriate command for running parallel jobs on your machine.

CleverLeaf's only explicit dependency is:

• SAMRAI (v. 3.6.3)

Other libraries, such as HDF5 and Boost, will need to be installed in order to build SAMRAI.

CleverLeaf uses a number of variables in the Make.inc to control compilation. These variables can be set as required to get CleverLeaf to compile on your system:

• COMPILER: The compiler vendor, used for selecting appropriate flags (INTEL or GNU).
• CXX: The C++ compiler to use.
• F90: The Fortran90 compiler to use.
• HDF_DIR: The location of HDF5.
• BOOST_DIR: The location of the Boost library (headers only).
• SAMRAI_DIR: The location of the SAMRAI library.

Once these variables have been set, CleverLeaf should build correctly. However, the CPPFLAGS, FFLAGS, and LDFLAGS can be modified if necessary.

CleverLeaf currently supports to targets: ref and openmp. The ref target builds the vanilla version of CleverLeaf using MPI only. The openmp target builds a hybrid version that uses both MPI and OpenMP.

Like CloverLeaf, CleverLeaf solves Euler's equations on a staggered grid, using an explicit, second-order accurate method. Each cell stores three values: energy, density, and pressure. A velocity vector is stored at each cell corner. The equations are solved in two dimensions. The following description of the equations is from the CloverLeaf documentation:

The compressible Euler equations are a set of three partial differential equations that describe the conservation of energy, mass and momentum in a system. CloverLeaf produces a second-order accurate solution using explicit finite volume methods. It first performs a Lagrangian step, using a predictor-corrector scheme to advance the solution forward by a calculated time delta. This step causes the mesh to move with fluid velocity, so an advective remap is used in order to return the mesh to its original state. A second-order Van Leer scheme is used, with the advective sweep being performed in the x and y directions for the energy, mass and momentum. The initial sweep direction alternates between steps, providing second order accuracy. The flow direction mush be calculated during the remap to allow data from the "upwind" direction to be used. Although the deformation of the grid does not actually move cell vertices, the average velocity on a cell face is used to approximate a flux through each face for the advection of material.

The compressible Euler equations form a hyperbolic system and therefore generate discontinuities in the form of shock waves. The second-order approximation will fail at these discontinuities and cause "ringing" in the solution. To avoid this, an artificial viscous pressure is used, which makes the solution first order in the presence of shock waves. This preserves monotonicity in the solution, by behaving as a simple addition to the pressure.

The timestep control uses the maximum sound speed as an upper bound for the time delta. The timestep is thus limited to the time it would take for the the highest speed sound wave to cross a cell. The timestep is then multiplied by a safety factor to preserve the stability of the solution. The timestep control contains two further tests: one to ensure that a vertex can't overtake another as the mesh deforms, and one to ensure that a cell cannot deform such that it's volume becomes negative.

In order to close the system of equations, we use an equation of state, which calculates the pressure and sound speed in a cell, given its energy and density. CloverLeaf uses the ideal gas equation of state with a gamma value of 1.4.

Currently, CloverLeaf only solves for a single material, although multiple states (pressures, densities, and velocities) of this material can exist in the problem domain. Support for multiple materials will be added into a future release.

The code is split into three main classes: LagrangianEulerianIntegrator, which is responsible for advancing the solution across the entire adaptive grid; LagrangianEulerianLevelIntegrator, which is responsible for advancing the solution on a single level; and Cleverleaf, which implements the LagrangianEulerianPatchStrategy interface, providing the methods needed to advance the solution on a single patch.

The physics in CleverLeaf uses the Fortran kernel functions written for CloverLeaf, and applies them to each patch in the adaptive hierarchy. Control code has been added which adapts the grid and synchronises the different levels of refinement. To coarsen the field variables, two additional operators have been added: CartesianCellDoubleMassWeightedAverage, and CartesianCellDoubleVolumeWeightedAverage. These are used to conservatively coarsen energy and pressure.

Cells are tagged based on three criteria: energy gradient, density gradient, and artificial viscosity value. Please see Cleverleaf.h for further documentation on how to control this tagging.

All header files contain detailed comments, and the make doc target can be used to build the documentation using Doxygen. Documentation for the current release version can be found at: