Three embedded techniques for finite element heat flow problem with embedded discontinuities

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-017-1382-7The present paper explores the solution of a heat conduction problem considering discontinuities embedded within the mesh and aligned at arbitrary angles with respect to the mesh edges. Three alternative approaches are proposed as solutions to the problem. The difference between these approaches compared to alternatives, such as the eXtended Finite Element Method (X-FEM), is that the current proposal attempts to preserve the global matrix graph in order to improve performance. The first two alternatives comprise an enrichment of the Finite Element (FE) space obtained through the addition of some new local degrees of freedom to allow capturing discontinuities within the element. The new degrees of freedom are statically condensed prior to assembly, so that the graph of the final system is not changed. The third approach is based on the use of modified FE-shape functions that substitute the standard ones on the cut elements. The imposition of both Neumann and Dirichlet boundary conditions is considered at the embedded interface. The results of all the proposed methods are then compared with a reference solution obtained using the standard FE on a mesh containing the actual discontinuity.Peer ReviewedPostprint (author's final draft

A framework for developing finite element codes for multi- disciplinary applications

The world of computing simulation has experienced great progresses in recent years and requires more exigent multidisciplinary challenges to satisfy the new upcoming demands. Increasing the importance of solving multi-disciplinary problems makes developers put more attention to these problems and deal with difficulties involved in developing software in this area. Conventional finite element codes have several difficulties in dealing with multi-disciplinary problems. Many of these codes are designed and implemented for solving a certain type of problems, generally involving a single field. Extending these codes to deal with another field of analysis usually consists of several problems and large amounts of modifications and implementations. Some typical difficulties are: predefined set of degrees of freedom per node, data structure with fixed set of defined variables, global list of variables for all entities, domain based interfaces, IO restriction in reading new data and writing new results and algorithm definition inside the code. A common approach is to connect different solvers via a master program which implements the interaction algorithms and also transfers data from one solver to another. This approach has been used successfully in practice but results duplicated implementation and redundant overhead of data storing and transferring which may be significant depending to the solvers data structure. The objective of this work is to design and implement a framework for building multi-disciplinary finite element programs. Generality, reusability, extendibility, good performance and memory efficiency are considered to be the main points in design and implementation of this framework. Preparing the structure for team development is another objective because usually a team of experts in different fields are involved in the development of multi-disciplinary code. Kratos, the framework created in this work, provides several tools for easy implementation of finite element applications and also provides a common platform for natural interaction of its applications in different ways. This is done not only by a number of innovations but also by collecting and reusing several existing works. In this work an innovative variable base interface is designed and implemented which is used at different levels of abstraction and showed to be very clear and extendible. Another innovation is a very efficient and flexible data structure which can be used to store any type of data in a type-safe manner. An extendible IO is also created to overcome another bottleneck in dealing with multi-disciplinary problems. Collecting different concepts of existing works and adapting them to coupled problems is considered to be another innovation in this work. Examples are using an interpreter, different data organizations and variable number of dofs per node. The kernel and application approach is used to reduce the possible conflicts arising between developers of different fields and layers are designed to reflect the working space of different developers also considering their programming knowledge. Finally several technical details are applied in order to increase the performance and efficiency of Kratos which makes it practically usable. This work is completed by demonstrating the framework’s functionality in practice. First some classical single field applications like thermal, fluid and structural applications are implemented and used as benchmark to prove its performance. These applications are used to solve coupled problems in order to demonstrate the natural interaction facility provided by the framework. Finally some less classical coupled finite element algorithms are implemented to show its high flexibility and extendibility

An Object-oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications

The objective of this work is to describe the design and implementation of a framework for building multi-disciplinary finite element programs. The main goals are generality, reusability, extendibility, good performance and memory efficiency. Another objective is preparing the code structure for team development to ensure the easy collaboration of experts in different fields in the development of multi-disciplinary applications. Kratos, the framework described in this work, contains several tools for the easy implementation of finite element applications and also provides a common platform for the natural interaction of different applications. To achieve this, an innovative variable base interface is designed and implemented. This interface is used at different levels of abstraction and showed to be very clear and extendible. A very efficient and flexible data structure and an extensible IO are created to overcome difficulties in dealing with multi-disciplinary problems. Several other concepts in existing works are also collected and adapted to coupled problems. The use of an interpreter, of different data layouts and variable number of dofs per node are examples of such approach. In order to minimize the possible conflicts arising in the development, a kernel and application approach is used. The code is structured in layers to reflect the working space of developers with different fields of expertise. Details are given on the approach chosen to increase performance and efficiency. Examples of application of Kratos to different multidisciplinary problems are presented in order to demonstrate the applicability and efficiency of the new object oriented environment

Three embedded techniques for finite element heat flow problem with embedded discontinuities

The present paper explores the solution of a heat conduction problem considering discontinuities embedded within the mesh and aligned at arbitrary angles with respect to the mesh edges. Three alternative approaches are proposed as solutions to the problem. The difference between these approaches compared to alternatives, such as the eXtended Finite Element Method (X-FEM), is that the current proposal attempts to preserve the global matrix graph in order to improve performance. The first two alternatives comprise an enrichment of the Finite Element (FE) space obtained through the addition of some new local degrees of freedom to allow capturing discontinuities within the element. The new degrees of freedom are statically condensed prior to assembly, so that the graph of the final system is not changed. The third approach is based on the use of modified FE-shape functions that substitute the standard ones on the cut elements. The imposition of both Neumann and Dirichlet boundary conditions is considered at the embedded interface. The results of all the proposed methods are then compared with a reference solution obtained using the standard FE on a mesh containing the actual discontinuity

A robust algorithm for implicit description of immersed geometries within a background mesh

The paper presents a robust algorithm, which allows to implicitly describe and track immersed geometries within a background mesh. The background mesh is assumed to be unstructured and discretized by tetrahedrons. The contained geometry is assumed to be given as triangulated surface. Within the background mesh, the immersed geometry is described implicitly using a discontinuous distance function based on a level-set approach. This distance function allows to consider both, “double-sided” geometries like membrane or shell structures, and “single-sided” objects for which an enclosed volume is univocally defined. For the second case, the discontinuous distance function is complemented by a continuous signed distance function, whereas ray casting is applied to identify the closed volume regions. Furthermore, adaptive mesh refinement is employed to provide the necessary resolution of the background mesh. The proposed algorithm can handle arbitrarily complicated geometries, possibly containing modeling errors (i.e., gaps, overlaps or a non-unique orientation of surface normals). Another important advantage of the algorithm is the embarrassingly parallel nature of its operations. This characteristic allows for a straightforward parallelization using MPI. All developments were implemented within the open source framework “KratosMultiphysics” and are available under the BSD license. The capabilities of the implementation are demonstrated with various application examples involving practice-oriented geometries. The results finally show, that the algorithm is able to describe most complicated geometries within a background mesh, whereas the approximation quality may be directly controlled by mesh refinement.Peer ReviewedPostprint (published version

A cut finite element method for the solution of the full-potential equation with an embedded wake

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-018-1624-3Potential flow solvers represent an appealing alternative for the simulation of non-viscous subsonic flows. In order to deliver accurate results, such techniques require prescribing explicitly the so called Kutta condition, as well as adding a special treatment on the “wake” of the body. The wake is traditionally modelled by introducing a gap in the CFD mesh, which requires an often laborious meshing work. The novelty of the proposed work is to embed the wake within the CFD domain. The approach has obvious advantages in the context of aeroelastic optimization, where the position of the wake may change due to evolutionary steps of the geometry. This work presents a simple, yet effective, method for the imposition of the embedded wake boundary condition. The presented method preserves the possibility of employing iterative techniques in the solution of the linear problems which stem out of the discretization. Validation and verification of the solver are performed for a NACA 0012 airfoil.Peer ReviewedPostprint (author's final draft

A robust algorithm for implicit description of immersed geometries within a background mesh

The paper presents a robust algorithm, which allows to implicitly describe and track immersed geometries within a background mesh. The background mesh is assumed to be unstructured and discretized by tetrahedrons. The contained geometry is assumed to be given as triangulated surface. Within the background mesh, the immersed geometry is described implicitly using a discontinuous distance function based on a level-set approach. This distance function allows to consider both, “double-sided” geometries like membrane or shell structures, and “single-sided” objects for which an enclosed volume is univocally defined. For the second case, the discontinuous distance function is complemented by a continuous signed distance function, whereas ray casting is applied to identify the closed volume regions. Furthermore, adaptive mesh refinement is employed to provide the necessary resolution of the background mesh. The proposed algorithm can handle arbitrarily complicated geometries, possibly containing modeling errors (i.e., gaps, overlaps or a non-unique orientation of surface normals). Another important advantage of the algorithm is the embarrassingly parallel nature of its operations. This characteristic allows for a straightforward parallelization using MPI. All developments were implemented within the open source framework “KratosMultiphysics” and are available under the BSD license. The capabilities of the implementation are demonstrated with various application examples involving practice-oriented geometries. The results finally show, that the algorithm is able to describe most complicated geometries within a background mesh, whereas the approximation quality may be directly controlled by mesh refinement

A cut finite element method for the solution of the full-potential equation with an embedded wake

Potential flow solvers represent an appealing alternative for the simulation of non-viscous subsonic flows. In order to deliver accurate results, such techniques require prescribing explicitly the so called Kutta condition, as well as adding a special treatment on the “wake” of the body. The wake is traditionally modelled by introducing a gap in the CFD mesh, which requires an often laborious meshing work. The novelty of the proposed work is to embed the wake within the CFD domain. The approach has obvious advantages in the context of aeroelastic optimization, where the position of the wake may change due to evolutionary steps of the geometry. This work presents a simple, yet effective, method for the imposition of the embedded wake boundary condition. The presented method preserves the possibility of employing iterative techniques in the solution of the linear problems which stem out of the discretization. Validation and verification of the solver are performed for a NACA 0012 airfoil.&nbsp

Open tools for electromagnetic simulation programs

Purpose The aim of the paper is to propose three computer tools to create electromagnetic simulation programs: GiD, Kratos and EMANT. Design/methodology/approach The paper presents a review of numerical methods for solving electromagnetic problems and presentation of the main features of GiD, Kratos and EMANT. Findings The paper provides information about three computer tools to create electromagnetic simulation packages: GiD (geometrical modeling, data input, visualisation of results), Kratos (C++ library) and EMANT (finite element software for solving Maxwell equations). Research limitations/implications The proposed platforms are in development and future work should be done to validate the codes for expecific problems and to provide extensive manual and tutorial information. Practical implications The tools could be easily learnt by different user profiles: from end‐users interested in simulation programs to developers of simulation packages. Originality/value This paper offers an integrated vision of open and easily customisable tools for the demands of different users profiles.   &nbsp

Realizing CoSimulation in and with a multiphysics framework

Simulating coupled problems using a multiphysics framework is different from the classical approach using dedicated coupling tools. It can have several advantages such as reduced memory footprint or more efficient communication between the involved solvers. The realization of coupled simulations with a multiphysics framework is presented together with important details of the software design such as data management, data communication, mapping, and distributed computing. Several examples from different physical disciplines with coupling internal and external solvers are shown