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Navier-Stokes Cartesian
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Description: NaSCar (Navier-Stokes Cartesian) is a research software, written in C and based on Petsc, to model numerically a wide range a multiphysics problems. The core is the incompressible Navier-Stokes equations discretized in space on a Cartesian mesh using Finite Differences and a temporal integration based on the Chorin and Temam scheme. Several new approaches to deal with fluid-structure and fluid-fluid interfaces have been developped including collison models and high order level set methods together with high order reinitialization. Elastic structures can be modeled in a Lagrangian way, or using a fully coupled Eulerian approach (with Mooney Rivlin model, see last figure).
One specificy of the code is toward drag and drop simulation. Any obstacle can be loaded in a simple way (stl, obj, or B-splines user defined bodies), and the simulation can start directly without considering any costly meshing and adaptation steps.
Indeed, all the simulations below are run with the exact same code, with only different input files (*.DAT)  defining the geoemtries and physical parameters.
The NaSCar solver will be soon distributed in Open Source.

List of the main fonctionalities

Libraries to generate obstacle profiles
 - Import of discrete geometry and regular meshing of this geometry,
 - Generation of 3D profiles by B-splines (fish, lines, ...),
 - Masks and characteristic functions

Fluid/structure interaction libraries,

 - Computation of forces and moments, Euler-quaternion angles,
 - One-way: imposed deformation of obstacles and displacement by Newton's laws,
 - Two-way: strongly implicit coupling, elastic beam structure, Eulerian elasticity
 - Eulerian elasticity: Extrapolation of the backward characteristics

Librairies for structure/structure interaction,

 - Lubrication and collision model for spherical and non-spherical obstacles (see TEST4)

Libraries to capture and track interfaces,

 - Generation of a level set function from any geometry,
 - Transport of the level set function (WENO5 and RK3 TVD),
 - Reinitialiszation to the signed distance function (Eikonale with relaxation),
 - Contour selection to ensure volume conservation

Libraries to solve the Navier-Stokes equations,

 - Incremental projection method of the predictor-corrector type (order 2),
 - Adams-Bashford - Crank-Nicholson, Semi-Lagrangian,
 - Volume penalization (order 1),
 - Immersed boundaries (order 2),
 - Hybrid IPC method (order 2),
 - Bifluid with surface tension: CSF and GFM methods (order 1), sharp method (order 2),
 - LES Smagorinsky-Lilly turbulence model

Examples of actual simulations with NaSCar (the movies are built with paraview)

Boat ride: the boat geometry is given by an obj file

Snake swimming: user defined body shape and swimming law

Dolphin jump: real dolphin shape from stp file with user defined swimming law

Fish swimming with collisions

LVAD prototype with a bioinspired elastic membrane activated with a forced holder
(inspired by the one developed by Corwave)

Numerical Enablers on OctreeS
Open Source

Descrpition: NEOS (Numerical Enablers on OctreeS) is a library written in C++.

NEOS is a software framework for numerically modeling multiphysics problems on Hierarchical Cartesian meshes (quadtree in 2D and octree in 3D).

NEOS is based on the bitpit library (

NEOS provides :

 - the creation and parallel management of hierarchical Cartesian meshes (2D quadtree or 3D octree)
 - global or local mesh refinement (based on a level-set distance or other physical criteria)
 - management of several mobile geometries in an analytical or explicit form (STL files or others)
 - computation of the level-set of these geometries at any point of the mesh
 - 2D/3D differential operators (gradient, Laplacian, Hessian, ...)
 - different 2D/3D interpolators (bilinear, radial basis functions RBF)
 - an API for different solvers (currently with PETSC)
 - a complete interface in Python3

The library is still in development, and ADER-DG solvers will be soon integrated to solve a wide variety of applicatons.

Example with mesh adapation:

LVAD like Pump (2D-axi):
the mesh adaptation, the construction and resolution of Poisson equation, the gradients computation, and the transport of the Level Set functions are part of the NEOS library.
(the simulation is done by Antoine Fondaneche during his PhD)