## WP1 Embedded methods

### Objectives

The work package aims to deliver the CFD capabilities needed for the accurate solution of problems including embedded objects. The possibility of considering exact geometries, and to map to and from such discretization is considered as a part of the WP.

The package builds on the top of pre-existing capabilities present in the parallel codes Kratos and FEMPAR, which already proved their scalability in previous European projects. Additional features will be added to the existing models depending of the specific characteristic of UQ and Optimization under Uncertainties.

### Tasks

#### Task 1.1: Development of geometry kernel for Trimmed NURBS

The objective of this task is to enable the CFD solvers to include complex geometries, described by unmodified NURBS geometry. Such task requires the capability of importing NURBS geometries through a properly defined input format, as well as making available computational kernels to ease the handling of operations (for example tessellation) of the geometry. The outcome of the task will be the development of an API able to read complex models and make it available to the solution kernels.

#### Task 1.2: Development and deployment of signed distance calculation routines from the exact geometry

This task provides the capability to effectively compute the distance from the surface of an embedded geometry. This includes the development of raytracing approaches to enable inside/outside tests for complex geometries. Such tests will be constructed implementing a full set of hierarchical techniques to achieve the necessary robustness.

#### Task 1.3: Routines for the definition of a target metrics

The objective of this task is to provide simple user-side routines to allow the easy definition of a target metric tensor, to be employed in refining the mesh. The routines will be designed to allow both the case of isotropic and anisotropic refinement. They will also include the capability to combine geometry-driven refinement (for example depending on the distance field) with simulation.

#### Task 1.4: Efficient implementation of embedded fluid technology on octree-based and unstructured meshes

The task will focus on the further development of existing embedded CFD solution capabilities. The enhancements will focus in this phase on taking full advantage of mesh adaptation, including also the necessary developments for effective dynamic load balancing.

#### Task 1.5: Development of parallel mapping routines to and from the exact geometry

The effective use of exact geometries in an embedded context requires the capability of mapping to and from the exact geometry. This includes both the capability to transfer information between multiple surfaces and between the surface and the volume discretization.

#### Task 1.6: Development of robust (and scalable) linear solvers for the embedded case

The solution of embedded problems typically faces difficulties when the intersection between the object and the mesh passes very close to the boundary of the volume element (“small-cut” instability). The focus of the workpackage is the developments of linear solvers which robustly remove such stability problem.