A FIC-based stabilized finite element formulation for turbulent flows

Cotela-Dalmau, Jordi; Rossi, Riccardo; Oñate, Eugenio

doi:10.1016/j.cma.2016.11.020

Cited by 10 publications

(12 citation statements)

References 36 publications

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“…condition and thus requires the use of stabilization techniques. Among the many successful approaches that can be found in the literature, such as the streamline upwind Petrov-Galerkin (SUPG) [39], the Galerkin/least-squares (GLS) [40] or the variational multiscales (VMS) family of techniques, featuring the algebraic subgrid scales (ASGS) [41][42][43] and orthogongal subscales (OSS) [44][45][46], in this work, we chose the finite increment calculus (FIC) [47][48][49][50]. In this regard, we note that owing to the segregated resolution strategy that we use, we only require the continuity equation to be stabilized [47].…”

Section: Discrete Form and Solution Strategymentioning

confidence: 99%

Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

Zorrilla,

Franci

2024

Engineering with Computers

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In this work, we present a novel unfitted mesh boundary strategy in the context of the Particle Finite Flement Method (PFEM) aiming to improve endemic limitations of the PFEM relative to boundary conditions treatment and mass conservation. In this new methodology, which we called Cut-PFEM, the fluid–wall interaction is not performed by adding interface elements, as is done in the standard PFEM boundaries. Instead, we use an implicit representation of (all or some of) the boundaries by introducing the use of a level set function. Such distance function detects the elements trespassing the (virtual) contours of the domain to equip them with opportunely boundary conditions, which are variationally enforced using Nitsche’s method. The proposed Cut-PFEM circumvents important issues associated with the standard PFEM contact detection algorithm, such as the artificial addition of mass to the computational domain and the anticipation of contact time. Furthermore, the Cut-PFEM represents a natural ground for the imposition of alternative wall boundary conditions (e.g., pure slip) which pose significant difficulties in a standard PFEM framework. Several numerical examples, featuring both no-slip and slip boundary conditions, are presented to prove the accuracy and robustness of the method in two-dimensional and three-dimensional scenarios.

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Section: Discrete Form and Solution Strategymentioning

confidence: 99%

Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

Zorrilla,

Franci

2024

Engineering with Computers

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“…Wind flow around the rectangular building is simulated using CFD analysis with the open-source Kratos Multiphysics tool. This involves a finite element method (FEM) formulation for flow problems based upon a VMS formulation[5]. The fluid domain is modeled with Fractional step elements.…”

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confidence: 99%

D7.2 Finalization of "deterministic" verification and validation tests

Apostolatos¹,

Rossi²,

Soriano³

2021

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This deliverable focus on the verification and validation of the solvers of Kratos Multiphysics which are used within ExaQUte. These solvers comprise standard body-fitted approaches and novel embedded approaches for the Computational Fluid Dynamics (CFD) simulations carried out within ExaQUte. Firstly, the standard body-fitted CFD solver is validated on a benchmark problem of high rise building - CAARC benchmark and subsequently the novel embedded CFD solver is verified against the solution of the body-fitted solver. Especially for the novel embedded approach, a workflow is presented on which the exact parameterized Computer-Aided Design (CAD) model is used in an efficient manner for the underlying CFD simulations. It includes: A note on the space-time methods Verification results for the body-fitted solver based on the CAARC benchmark Workflow consisting of importing an exact CAD model, tessellating it and performing embedded CFD on it Verification results for the embedded solver based on a high-rise building API definition and usage

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“…A local shock capturing technique was initially proposed by Hughes [85] and a review of shock capturing techniques can be found in Codina [36]. Other possibilities of the FIC-based formulations are explored to provide a shock capturing stabilization [43].…”

Section: Stabilized Formulations For the Shallow Water Equationsmentioning

confidence: 99%

“…In [141] l e is chosen as a vector, but in later publications such as [142] a generalized formulation for different values of n d and n b was presented. For the stabilization of the Navier-Stokes equations different projections of the element size over the velocity and over the velocity gradient have been proposed [43]. Here we will use index notation for the residual vector r in order to distinguish the indices that goes to n d or to n b .…”

Section: Fic Stabilizationmentioning

confidence: 99%

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Coupling shallow water models with three-dimensional models for the study of fluid-structure interaction problems using the particle finite element method

Maso Sotomayor

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(English) This thesis investigates numerical methods for the simulation of surface water flows, focusing on the interaction between the large scale and the local scale and its application to natural hazards. Several families of numerical methods for the approximation of large scale phenomena and the coupling with the local scale have been analyzed. The general motion of a fluid mass is governed by the Navier-Stokes equations, which can accurately solve the local scale phenomena. However, the same level of accuracy is not required by the large scale solution of the water-related events. In this context, the shallow water equations are defined. In contrast to the extensive use of the Finite Element Method for solving the Navier-Stokes equations, the shallow-water equations are usually solved with the Finite Volume Method. Thus, an effort have been done to solve both equations in an unified framework. The first part of this thesis is devoted to study stabilized formulations of Finite Element Method for the different forms of the shallow water equations. Stabilized formulations arise from the need to mitigate the various instabilities inherent in numerical approximations. The first source of instability is the incompatibility of the equal interpolation of the variables. The second source of instability is the presence of shocks due to the change of regime or hydraulic jumps. Finally, Gibbs oscillations may appear on the moving shoreline and monotonic properties of the physical system are lost by the numerical approximation. The second part of the thesis is committed to the coupling strategies of the numerical methods for the Navier-Stokes and the shallow water equations. The case of a coupling from the local scale to the large scale is analyzed. This type of coupling corresponds to the generation of cascading natural hazard. The proposed strategy combines a Lagrangian Navier Stokes multi-fluid solver with an Eulerian method based on the Boussinesq equations, an extension of the shallow water equations. Finally, the proposed technique is applied to the numerical simulation of landslide-generated impulse waves. The Particle Finite Element Method has been used to model the landslide runout, its impact against the water body and the consequent wave generation. The results of this fully-resolved analysis are stored at selected interfaces and then used as input for the modelling of waves propagation on the far-field. This one-way coupling scheme drastically reduces the computational cost of the analyses while maintaining high accuracy in reproducing the key phenomena of cascading natural hazards. (Español) En esta tesis se investigan métodos numéricos para la simulación de flujos de aguas superficiales, haciendo énfasis en la interacción entre las distintas escalas y su aplicación a desastres naturales. Se han analizado diversas familias de métodos numéricos para aproximar los fenómenos a gran escala y su acoplamiento con la escala local. El movimiento general de una masa de fluido se rige por las ecuaciones de Navier-Stokes, que pueden resolver con precisión los fenómenos a escala local. Sin embargo, la solución numérica a gran escala de dichos fenómenos, no requiere el mismo nivel de precisión. En este ámbito, se definen las acuaciones de agua poco profundas. En contraste con el amplio uso del Método de los Elementos Finitos para aproximar las ecuaciones de Navier-Stokes, las ecuaciones de aguas poco profundas se suelen resolver con el Método de los Volúmenes Finitos. Por ello, se ha realizado un esfuerzo para resolver ambas ecuaciones en un marco unificado. La primera parte de esta tesis está dedicada a estudiar formulaciones estabilizadas para el Método de los Elementos Finitos aplicado a las diferentes formas de las ecuaciones de aguas someras. Las formulaciones estabilizadas surgen de la necesidad de mitigar las diferentes inestabilidades inherentes a las aproximaciones numéricas. La primera fuente de inestabilidad es la incompatibilidad debida a la interpolación de las variables. La segunda fuente de inestabilidad es la presencia de discontinuidades debidos al cambio de régimen o a los saltos hidráulicos. Por último, pueden aparecer oscilaciones de Gibbs en la línea de costa en movimiento, dado que las propiedades monótonas del sistema físico se pierden por la aproximación numérica. La segunda parte de la tesis está dedicada a las estrategias de acoplamiento de los métodos numéricos para las ecuaciones de Navier-Stokes y de aguas poco profundas. Se ha analizado el caso de acoplamiento desde la escala local a la escala global. Este tipo de acoplamiento corresponde a la generación de desastres naturales en cascada. La estrategia propuesta combina un solver Lagrangiano de Navier Stokes para multi-fluidos con un método Euleriano basado en las ecuaciones de Boussinesq, una extensión de las ecuaciones de aguas someras. Finalmente, la técnica propuesta se ha aplicado a la simulación numérica de olas generadas por deslizamientos. El deslizamiento de ladera, su impacto contra la masa de agua y la consiguiente generación de olas se ha modelado con el Método de Elementos Finitios de Partículas. Los resultados de este análisis detallado se almacenan en las interfaces seleccionadas que, luego, se utilizan como punto de entrada para modelar la propagación de olas en el campo lejano. Este esquema de acoplamiento unidireccional reduce drásticamente el coste computacional, a la vez que se mantiene una alta precisión en la simulación de los fenómenos clave de desastres naturales.

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A FIC-based stabilized finite element formulation for turbulent flows

Cited by 10 publications

References 36 publications

Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

D7.2 Finalization of "deterministic" verification and validation tests

Coupling shallow water models with three-dimensional models for the study of fluid-structure interaction problems using the particle finite element method

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