pressio / pressio-demoapps

Suite of 1D, 2D, 3D demo apps of varying complexity with built-in support for sample mesh and exact Jacobians

Overview

pressio-demoapps is a library of 1D, 2D and 3D demo problems of varying complexity, ranging from a simple 1D linear advection, to 2D reaction-diffusion, and 3D Euler equations, and more.

Key features include:

• support for both C++ and Python
• cell-centered finite volume discretization with various numerical schemes and exact Jacobians
• focus on providing self-contained and well-defined problems
• built-in support for a sample mesh: this mean that one can evaluate the residual and Jacobian at a disjoint subset of the mesh cells (this is useful for intrusive ROMs, but in general for other purposes too)

Click below to check the documentation for more details:

Development status

pressio-demoapps is planned to be maintained in the long-term. Hopefully, more problems and features will be implemented. If you are interested in collaborating or would like to see a specific problem added, please reach out.

Questions?

Find us on Slack: https://pressioteam.slack.com or open an issue on github.

License and Citation

While we work on publishing this, if you use this code, please reference this Github page!

The full license is available here.

pressio-demoapps's Issues

add FD Jacobians

Currently only support evaluation of the RHS, need to add FD Jacobians to all classes

fix ambiguity in resolution for weno overloads

need to better constraint the templates in weno.hpp

add rankine-hugoniot function for determining pre/post-shock states

• related to #6
• function should accept prim vars on one side and return the prim on the other
• a test should be added to only test this function is correct

jacobians: add check to ensure nonzeros do not change from initialization

we need to ensure that # of nonzeros after initialization is the same as after first evaluation of jacobian.
this is because for Eigen, one can add elements, so we need to make sure we don't add new elements.

select face reconstruction order via constructor's arg

we currently select which order to use (1st, or 5th weno) based on the stencil size of the mesh provided. This is constraining a bit, since the 7 point stencil of the weno can support 1st order too.
So we need to add a way to select the order and then check that the selected order is compatible with the mesh provided.

cpp: add applyJacobian to cpp classes

doc: check math formulation for each problem page, add it if missing

Goal: self-explanatory

Steps:

• make a new branch from develop
• look inside pressio-demoapps/docs/src
• doc is written in rst
• fill math formulation for each problem
• once done, open PRs for individual problems, or for example groups of problems (e.g. one PR for 1d, one for 2d ,etc)

Building the documentaiton:

cd pressio-demoapps/docs
make html

then open index.html in a browser. If you rebuild, you can refresh the page.
To build, you need sphinx and some other things.

support for laplacian using FV

We should add diffusion such that it is consistent with the FV formulation.

Roe flux

Add Roe flux capability.

Following chapter 11 of "Riemann Solvers and Numerical Methods" by Toro, the algorithm should

1. Compute Roe averaged velocities, total enthalpy, and speed of sound
2. Compute Roe averaged eigenvalues using an analytical expression, potentially with an "entropy fix".
3. Compute the Roe averaged right eigenvectors using analytical expressions for each entry
4. Project the jump in each conserved quantity onto the right eigenvectors. Again, there are analytical expressions for this in Toro's book or Roe's original paper.
5. Compute fluxes using equations 11.27-11.29 in Toro.

All of this should be possible following the same API used for the Rusanov flux in pressiodemoapps/impl_apps/eulerCommon/fluxes.hpp

Important note: there is a typo in Roe's original paper! The right hand side of Equation 22b should be \delta u_4 - w * \delta u_1.

Jacobians!

• 1st order local Jacobians for Rusanov Flux
• Convert tests to gtest format
• Set up complex step derivative in tests
• Global Jacobian contruction
  • Dirichlet BCs
  • Neumann BCs
  • Reflection BCs
  • Periodic BCs
• Weno reconstruction contributions
• 1st order local Jacobians for Roe Flux

design a way to allow changing physical parameters

• advection velocity for 1d, but need to change impl since it assumes unitary velocity
• gas constant for euler
• shock angle and initial shock Mach for double mach
• all coefficients for shallow water (depends on #12)

openmp: finish impl and add details to doc

missing for 1d

bindings: operator (...) for pybind array_t is not efficient

The operator () for pybind::array_t in line 906 of this file is not efficient. I added this myself originally since natively array_t did not support it.
One reason behind the perf issue is that looking at the impl (traces back to the parent array class, see that same file), it still performs a bound check.

Problem is that inside pressio-demoapps, we are using this to access the graph entries. We should change things to use the mutable and mutable_unchecked that seem to perform well since these proxy classes do not perform bounds check. However, we need to figure out how to handle these proxies properly.

python has changed installation method, need to fix

should not do anymore python setup.py install but sometihing else.

in fact I get:

/usr/local/lib/python3.9/site-packages/setuptools/command/install.py:34: SetuptoolsDeprecationWarning: setup.py install is deprecated. Use build and pip and other standards-based tools.
  warnings.warn(

tests: move common scripts to toplevel dir to avoid duplication of stuff

mesh: enable nonperiodic BC

Modify script to enable non periodic BC

apps: revive shallow water eq problem

• update the Eigen-based swe problem class
• update the corresponding public include file
• add test for it

list of supported problems

Test problems below are partially taken from here
A list of specific references for each is shown below, and will be updated.

1D

• linear advection

  • use domain:[-1, 1]
  • IC either provided by user or default one is \phi = sin(\pi x)
  • BC: periodic

• Euler Smooth

  • use domain: [-1, 1]
  • default IC is \rho =1 + 0.2*sin(\pi x), u= 1, p = 1
  • BC: periodic
  • analytical density at time t : \rho =1 + 0.2*sin(\pi (x-t))

• Sod problem

  • use domain: [-0.5, 0.5]
  • IC:
    • x<=0: \rho =1, u= 1, p = 1
    • x>0 : \rho =0.125, u= 1, p = 0.1
  • BC: homogeneous Neumann

• Lax problem

  • use domain: [-5, 5]
  • IC:
    • x<=0: \rho = 0.445, u = 0.698, p = 3.528
    • x>0 : \rho = 0.5, u = 0., p = 0.571
  • BC: homogeneous Neumann

2D

• Euler Smooth

  • use domain: [-1, 1]^2
  • default IC is \rho =1 + 0.2*sin(\pi (x+y)), u = 1, v = 1, p = 1
  • BC: periodic
  • analytical density at time t : \rho =1. + 0.2*sin(\pi (x+y- 2 t))

• Sedov problem (full version, no symmetry use)

  • reference
  • use domain: [-0.6, 0.6]^2
  • BC: homogeneous Neumann on all boundaries
  • IC is a high pressure concentrated small spherical region of radius R = 2. * std::min(dx, dy)
    • r<=R: \rho =1, u = 0, v = 0, p = (\gamma-1)/(pi*R*R)
    • r>R : \rho =1, u = 0, v = 0, p = 5e-5
  • dx, dy are the cell widths and the factor of 2 is used to spread the source over 2 cells for numerical reasons, and r = sqrt(x^2+y^2) is the distance from the origin.

• Sedov problem (exploit symmetry to simulate only one quadrant)

  • use domain: [0, 1.2]^2
  • BC: reflective on y=0 and x=0 and homogeneous Neumann for x=1.2 and y=1.2
  • IC involves a small spherical region of radius R = 3. * std::min(dx, dy) with high pressure
    • r<=R: \rho =1, u = 0, v = 0, p = ((\gamma-1)* 0.851072)/(pi*R*R)
    • r>R : \rho =1, u = 0, v = 0, p = 2.5e-5
  • dx, dy are the cell widths, and r = sqrt(x^2+y^2) is the distance from the origin.

• Riemann problem

  • use domain: [0.0, 1.0]^2
  • BC: homogeneous Neumann on all boundaries
  • various initial conditions are supported:
    • IC 1:
      • x>=0.5, y>=0.5: \rho = 0.5313, u = 0, v = 0, p = 0.4
      • x<0.5, y>=0.5 : \rho = 1, u = 0.7276., v = 0, p = 1
      • x<0.5, y<0.5. : \rho = 0.8, u = 0, v = 0., p = 1
      • x>0.5, y<0.5. : \rho = 1., u = 0, v = 0.7276, p = 1
    • IC 2:
      • x>=0.8, y>=0.8 : \rho = 1.5, u = 0, v = 0, p = 1.5
      • x<0.8, y>=0.8 : \rho = 0.5323, u = 1.206, v = 0, p = 0.3
      • x<0.8, y<0.8 : \rho = 0.138, u = 1.206, v = 1.206, p = 0.029
      • x>0.8, y<0.8 : \rho = 0.5323, u = 0, v = 1.206, p = 0.3

• Double Mach reflection

  • in progress

• Wind tunnel with step

  • in progress

3D

• Euler Smooth

  • use domain: [-1, 1]^3
  • default IC is \rho = 1 + 0.2*sin(\pi (x+y+z)), u = 1, v = 1, w = 1, p = 1
  • BC: periodic
  • analytical density at time t : \rho =1 + 0.2*sin(\pi (x+y+z-3 t))

• Sedov problem (exploit symmetry to simulate only 1/8)

  • use domain: [0, 1.2]^3
  • BC: reflective on planes next to source, homogeneous Neumann for the others
  • IC involves a small spherical region of radius R = 3. * min(dx, dy, dz) with high pressure
    • r<=R: \rho =1, u = 0, v = 0, p = (3 (\gamma-1)* 0.851072)/(4 pi R^3)
    • r>R : \rho =1, u = 0, v = 0, p = 2.5e-5
  • dx, dy, dz are the cell widths, and r = sqrt(x^2+y^2+z^2) is the distance from the origin.

doc: more work on sample mesh and how it can be used

python script to visualize results

need to add a python script to visualize results

• 1D cases
• 2D cases

euler1d: ghost cells need to be fixed for sample mesh

currently assuming first and last cells are on boundary, but this does not work for sample mesh

reconstructor: make `operator()` non-templated

meshing: make stand-alone script to visualize

Curerntly, the code to plot the mesh is part of the generation. we need to extract it and makeing it self-contained.
So that generating the mesh and visualizing it are separate steps/scripts

list of problems/capability [do not close]

1D

• linear advection
  • rhs (1st/weno3/weno5)
  • first-order Jacobian
  • OpenMP
  • Python bindings
• diffusion reaction
  • rhs
  • Jacobian
  • OpenMP
  • Python bindings
• 1d Euler
  • rhs (1st/weno3/weno5)
  • first-order Jacobian
  • OpenMP
  • Python bindings

2D

• 2d euler
  • rhs (1st/weno3/weno5)
  • first-order Jacobian
  • OpenMP
  • Python bindings
• 2d swe
  • rhs (1st/weno3/weno5)
  • first-order Jacobian
  • OpenMP
  • Python bindings
• 2d diffusion-reaction
  • rhs
  • Jacobian
  • OpenMP
  • Python bindings
• 2d compre nav-sto
  • rhs (1st/weno3/weno5)
  • first-order Jacobian
  • OpenMP
  • Python bindings

3D

• 3d euler
  • rhs (1st/weno3/weno5)
  • first-order Jacobian
  • OpenMP
  • Python bindings
• 3d compre nav-sto
  • rhs (1st/weno3/weno5)
  • first-order Jacobian
  • OpenMP
  • Python bindings

Fix CMakeLists for eigen_euler_rusanov_flux_jacobians tests

CMakeLists links main1d.cc to both the 2d and 3d tests; making an issue so we don't forget.

CI: create actions to run tests on every push

need to add action for testing.
since we have C++ and Python code, the CI should cover both.
Check the readme for how to build/run the C++ tests and bindings.

doc: fill content for end-to-end example in C++

2d euler: 1st-order jacobian for double mach at top boundary is wrong

seems we have everything right except for top boundary

euler1d: non periodic BC needs another test

fix impl namespaces to be consistent

we need to standardize the naming for the impl namespace for each problem

1d problems: refactor impl so that boundary cells are computed first

in 2d,3d we first handle the boundary cells, and then the inner ones.
We should do similarly for 1d.
That allows us to use the auxiliary stencil vector for boundary cells but just use the state (without copying data) for the inner cells.

fix issue with enabling openmp for binding

seems like cmd line option passed to install command does not work

meshing: enable/verify stencil size 3,5,7

Change name of the Python script which builds library

TODO:

• there is a need of the name change for a Python script which builds dynamic library with CMake
• name build confuses Python interpreter and python -m build is not using build package, to actually build the , but is running the script
• changes needs to be done in CI as well

Add shallow water equation examples to pressio demo apps

Add the shallow water equations along with a case setup to pressio demo apps. To do:

• Add code for SWE equations
• test for the velocity function in the case of full mesh
• test for the velocity function in the case of sample mesh
• test for the full time integration
• validate against existing SWE solver

add linear advection

support python bindings via pybind11

Obj: to create problem classes in python that use the c++ implementation

how:

• follow how we did bindings for pressio-tools or pressio4py
• should be relatively easy to do , maybe some issues can come up related to sparse jacobians

Priorites:

• Sedov problem for John to use

fix warning

/home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/functor_reconstruct_from_state.hpp(54): warning #858: type qualifier on return type is meaningless
    const ReconstructionScheme reconstructionScheme() const{
    ^

In file included from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/advection_1d_prob_class.hpp(6),
                 from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/advection.hpp(17),
                 from /home/fnrizzi/pressio-demoapps/src_py/main_binder.cc(14):
/home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/functor_reconstruct_from_state.hpp(139): warning #858: type qualifier on return type is meaningless
    const ReconstructionScheme reconstructionScheme() const{
    ^

In file included from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/euler_1d_prob_class.hpp(11),
                 from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/euler1d.hpp(22),
                 from /home/fnrizzi/pressio-demoapps/src_py/main_binder.cc(16):
/home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/functor_reconstruct_from_stencil.hpp(51): warning #858: type qualifier on return type is meaningless
    const ReconstructionScheme reconstructionScheme() const{
    ^

In file included from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/euler_1d_prob_class.hpp(11),
                 from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/euler1d.hpp(22),
                 from /home/fnrizzi/pressio-demoapps/src_py/main_binder.cc(16):
/home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/functor_reconstruct_from_stencil.hpp(115): warning #858: type qualifier on return type is meaningless
    const ReconstructionScheme reconstructionScheme() const{
    ^

In file included from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/euler_1d_prob_class.hpp(11),
                 from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/euler1d.hpp(22),
                 from /home/fnrizzi/pressio-demoapps/src_py/main_binder.cc(16):
/home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/functor_reconstruct_from_stencil.hpp(242): warning #858: type qualifier on return type is meaningless
    const ReconstructionScheme reconstructionScheme() const{
    ^

In file included from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/euler_1d_prob_class.hpp(11),
                 from /home/fnrizzi/pressio-demoapps/include/pressiodemoapps/euler1d.hpp(22),
                 from /home/fnrizzi/pressio-demoapps/src_py/main_binder.cc(16):
/home/fnrizzi/pressio-demoapps/include/pressiodemoapps/./impl/functor_reconstruct_from_stencil.hpp(395): warning #858: type qualifier on return type is meaningless
    const ReconstructionScheme reconstructionScheme() const{
    ^

double mach: WENO5 not working

Using same BCs as first and WENO3, still gets unstable right away near wedge location.
Currently, the code throws if user selects WENO5 for double mach.

doc: need to explain how dofs are stored

• make clear how dofs are stored, the difference between primitive and convervative, etc

cpp: cleanup constructors

need to change how constructors are exposed now. We have a mix of things: inside includable headers we have some that pretty much as just variadic and forward everything to problem classes. We need to expose public constructors ONLY in the includable headers.

doc: need to add all include statements for C++

support mix of periodic and non periodic

Need to change:

• meshing script: should be pretty easy to change mesh scripts to do this
• mesh class in the code (now periodic means fully periodic along all axes)

add double Mach reflection

References:

• https://homepages.dias.ie/jmackey/jmac/node10.html

• others?

• problem setup: domain, BC, etc

• add initial condition for the problem here: https://github.com/Pressio/pressio-demoapps/blob/main/include/impl/euler2d/initial_condition.hpp

• add Eigen implementation:

  • file to use : https://github.com/Pressio/pressio-demoapps/blob/main/include/impl/euler2d/eigen_app.hpp
  • use a proper value for probid (see the other cases) to identify this particular problem

• add the public alias for this problem here: https://github.com/Pressio/pressio-demoapps/blob/main/include/euler.hpp

• add a test for it, use the Sedov test as template: https://github.com/Pressio/pressio-demoapps/tree/main/tests/sedov2d

  • to create the mesh files, see python script here
    If we use the domain in the reference above, the command is something:

  python create_full_mesh.py --outDir <where-youwant-the-mesh-files> \
  -s 7 --bounds 0.0 0.325 0.0 1.0 --periodic false -n 260 80

  the -s 7 is to create a mesh with a 7 point stencil.

meshing: support a step inside rectangular domain

• the simple meshing file needs to be extented to support a step inside

• the mesh for the domain wth the step should still be uniform

provide C++ cmake templates that one can use to solve problems

Need to add for:

• explicit time stepping
• implicit

2d diff reaction seems broken with openmp in Python

i get a segfault from the test

complte create mesh helper fncs in create_full_mesh_for.py

add more methods to mesh object class

• min/max for mesh coordinates
• boolean to check if graph has periodic BC built in
  others?

cpp: check that mesh provided is consistent with problem selected

Since we have specific problems, we need to add inside the impl classes checks such that when the problems are constucted , the mesh object passed in satisfies the physical bounds for that specific problem

e.g., for the Euler2d:

explicit EigenApp2d(const mesh_t & meshObj, int icId = 1)  
: meshObj_(meshObj), icId_(icId)  {    
 if (probid == 1){ 
   // throw if domain not compatible with 2d Sedov, else throw
 }
else if (probid==2){
   // throw if domain not compatible with 2d Riemann 
}
 ///
}