A GPU Accelerated Framework for Partitioned Solution of Fluid-Structure Interaction Problems

We present a GPU-accelerated solver for the partitioned solution of fluid-structure interaction (FSI) problems. Independent scalable fluid and structure solvers are coupled by a library which handles the inter-code data communication, mapping and equation coupling. A coupling strategy is incorporated which allows accelerating expensive components of the coupled framework by offloading them to GPUs. To prove the efficiency of the proposed coupling strategy in conjunction with the offloading scheme, we present a numerical performance analysis for a complex test case in the filed of biomedical engineering. The numerical experiments demonstrate an excellent speed-up in the accelerated kernels (up to 133 times) which results in 6 to 8 times faster overall simulations. In addition, we observed a very good reduction in total simulation time by increasing the exploited compute nodes up to 8 (complete machine capacity).We thank the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) for supporting this work by funding - EXC2075 – 390740016 under Germany’s Excellence Strategy. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech). This work was also financially supported by • priority program 1648 - Software for Exascale Computing 214 (ExaFSA - Exascale Simulation of Fluid-Structure-Acoustics Interactions) of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), • Ministerio de Economía y Competitividad, Secretaría de Estado de Investigacion, Desarrollo e ´ Innovacion, Spain (ENE2017-88697-R). ´ The performance measurements were carried out on the Vulcan cluster at the High-Performance Computing Center Stuttgart (HLRS). The authors wish to thank HLRS for compute time and technical support.Peer ReviewedPostprint (published version

A Robin-Neumann Scheme with Quasi-Newton Acceleration for Partitioned Fluid-Structure Interaction

The Dirichlet-Neumann scheme is the most common partitioned algorithm for fluid-structure interaction (FSI) and offers high flexibility concerning the solvers employed for the two subproblems. Nevertheless, it is not without shortcomings: To begin with, the inherent added-mass effect often destabilizes the numerical solution severely. Moreover, the Dirichlet-Neumann scheme cannot be applied to FSI problems in which an incompressible fluid is fully enclosed by Dirichlet boundaries, as it is incapable of satisfying the volume constraint. In the last decade, interface quasi-Newton methods have proven to control the added-mass effect and substantially speed up convergence by adding a Newton-like update step to the Dirichlet-Neumann coupling. They are, however, without effect on the incompressibility dilemma. As an alternative, the Robin-Neumann scheme generalizes the fluid's boundary condition to a Robin condition by including the Cauchy stresses. While this modification in fact successfully tackles both drawbacks of the Dirichlet-Neumann approach, the price to be paid is a strong dependency on the Robin weighting parameter, with very limited a priori knowledge about good choices. This work proposes a strategy to merge these two ideas and benefit from their combined strengths. The effectiveness of this new quasi-Newton-accelerated Robin-Neumann scheme is demonstrated for different FSI simulations and compared to both Robin- and Dirichlet-Neumann variants.Comment: Keywords: Partitioned Fluid-Structure Interaction, Robin-Neumann Scheme,Interface Quasi-Newton Method

Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives

Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments. \ua9 The author

Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: Overview and perspectives

Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments

Developing numerical methods for fully-coupled nonlinear fluid-structure interaction problems

This thesis is dedicated to developing numerical methods to solve fluid-structure interaction (FSI) problems. FSI features in a vast range of physical systems and has a wide application in engineering. The work of this thesis is focused on the partitioned methods, mostly due to their features of modularity, robustness and reliability. In a partitioned approach, separate solvers are used for the fluid and structural sub-problem domains and a coupling method is devised to account for their mutual interaction. Moreover, the thesis is focused on FSI problems with strong added-mass effect, which are more challenging to solve numerically. For such FSI problems, normally an implicit partitioned method is used which enforces the coupling conditions on the interface through coupling iterations between the fluid and structural solvers. However, these methods are computationally expensive. In this work we follow a semi-implicit approach to develop stable, efficient and accurate numerical methods for FSI problems. In these methods, the fluid pressure term is segregated and strongly coupled to the structure via coupling iterations. However, the remaining fluid terms and the geometrical nonlinearities are treated explicitly. Strong coupling of the fluid pressure term provides for the stability of the method in FSI problems with strong added-mass effect, while loose coupling of the remaining terms reduces the computational cost of the simulations. The work of this thesis could be divided into three major parts. In the first part, we have developed a simple, efficient and robust semi-implicit coupling method for FSI problems with strong added-mass effect. The proposed method is simple and modular. An extensive set of numerical tests were carried out and the results were compared both to literature data (numerical and experimental), as well as domestic results obtained by using a fully-implicit coupling method. Results showed that the proposed method considerably reduces the computational cost of the simulations without degrading the stability or accuracy of the solution. Moreover, the robustness of the method is demonstrated through numerical tests. Furthermore, we have tried to further analyze the semi-implicit methods in order to gain a better understanding of several unaddressed issues concerning different aspects of these methods. The second major part of this thesis is focused on the temporal accuracy of the semi-implicit coupling methods for FSI problems. The semi-implicit methods in the literature appear to be only first-order in time. Most semi-implicit methods rely on using a projection method for the fluid equations, while extending the temporal accuracy of the projection methods is not straightforward. Moreover, mesh-conforming FSI solution methods require solving the ALE form of the Navier-Stokes equations on a moving mesh, which does not necessarily preserve the order of accuracy of the method on a fixed grid. Furthermore, if the FSI coupling technique is not properly designed, the second-order accuracy for the coupled problem is not guaranteed, even though each sub-problem possessed such accuracy. In this work, we have proposed a second-order time accurate semi-implicit method for FSI problems and demonstrated its second-order accuracy through rigorous numerical tests. The last major part of this thesis is concerned with computational efficiency and parallel scalability of the developed methods for numerical solution of complex FSI problems on massively-parallel supercomputers. We have presented a scalable parallel framework for partitioned solution of FSI problems through multi-code coupling. Two instances of our in-house software is used to solve the fluid and structural sub-problems. The communication between the single-physics solvers are carried out using an external coupling library. Parallel efficiency and scalability of the coupled framework is demonstrated in solving practical FSI test cases.Esta tesis está dedicada al desarrollo de métodos numéricos para resolver problemas de interacción de fluido-estructura (FSI). Esta fenomenología aparece en una amplia gama de sistemas físicos y aplicaciones en ingeniería. El trabajo se centra en los métodos de partición, principalmente debido a sus características de modularidad, robustez y fiabilidad. En estos métodos se utilizan solvers distintos para los dominios de fluido y estructura, siendo esencial la técnica de acoplamiento para tener en cuenta su interacción mutua. Además, la tesis se centra en los problemas del FSI con un fuerte efecto de "masa agregada", que son más complejos de resolver numéricamente. Normalmente se usa un método de partición implícito que impone las condiciones de acoplamiento en la interfaz a través de iteraciones entre los solucionadores de fluido y de estructura. Sin embargo, estos métodos son computacionalmente costosos. En esta tesis seguimos un enfoque semi-implícito que permite métodos numéricos estables, eficientes y precisos, en donde el término de presión del fluido está segregado y fuertemente acoplado a la estructura a través de iteraciones de acoplamiento. Sin embargo, los términos fluidos restantes y las no linealidades geométricas se tratan explícitamente. El fuerte acoplamiento del término de presión del fluido proporciona la estabilidad del método en problemas de FSI con un fuerte efecto de masa agregada, mientras que el acoplamiento de los términos restantes reduce el coste computacional. La tesis se divide en tres partes principales. En la primera se desarrolla un método de acoplamiento semi-implícito eficiente y robusto para problemas con un fuerte efecto de masa agregada. El método propuesto es simple y modular. Se llevó a cabo un extenso conjunto de pruebas numéricas. Los resultados se compararon con datos de la literatura (numéricos y experimentales), así como con resultados propios obtenidos mediante el uso métodos de acoplamiento totalmente implícitos. Las pruebas realizadas mostraron que el método propuesto reduce considerablemente el coste computacional de las simulaciones sin degradar su estabilidad y precisión. Además, se ha analizado más a fondo los métodos semi-implícitos con el fin de obtener una mejor comprensión de varias cuestiones no abordadas en relación con algunos aspectos de estos métodos. La segunda parte de esta tesis se centra en la precisión temporal de los métodos de acoplamiento semi-implícitos para problemas de FSI. La mayoría de los métodos semi-implícitos propuestos se basan en el uso de técnicas de proyección para las ecuaciones del fluido, con aproximaciones de primer orden temporal, no siendo sencilla su extensión a alto orden. Además, los métodos de malla-conforme requieren la resolución ALE de las ecuaciones de Navier-Stokes en mallas en movimiento, lo que no necesariamente conserva el orden de precisión del método en una cuadrícula fija. Si la técnica de acoplamiento FSI no está diseñada adecuadamente, no se puede garantizar la precisión de segundo orden para el problema acoplado, aunque cada sub-problema posea tal precisión. En este trabajo se propone un método semi-implícito de segundo orden temporal para este tipo de problemas, y se demuestra dicha precisión a través de rigurosas pruebas numéricas. La última parte de esta tesis se refiere a la eficiencia computacional y la escalabilidad paralela de los métodos desarrollados para la solución numérica de problemas complejos de FSI en supercomputadoras masivamente paralelas. Se presenta un marco paralelo escalable para la solución particionada a través del acoplamiento de múltiples códigos. Se utilizan dos instancias de nuestro software interno para resolver los sub-problemas de fluidos y estructurales. La comunicación entre los solucionadores de física simple se realiza mediante una biblioteca de acoplamiento externa...Postprint (published version

Development of robust and efficient solution strategies for coupled problems

Det er mange modeller i moderne vitenskap hvor sammenkoblingen mellom forskjellige fysiske prosesser er svært viktig. Disse finner man for eksempel i forbindelse med lagring av karbondioksid i undervannsreservoarer, flyt i kroppsvev, kreftsvulstvekst og geotermisk energiutvinning. Denne avhandlingen har to fokusområder som er knyttet til sammenkoblede modeller. Det første er å utvikle pålitelige og effektive tilnærmingsmetoder, og det andre er utviklingen av en ny modell som tar for seg flyt i et porøst medium som består av to forskjellige materialer. For tilnærmingsmetodene har det vært et spesielt fokus på splittemetoder. Dette er metoder hvor hver av de sammenkoblede modellene håndteres separat, og så itererer man mellom dem. Dette gjøres i hovedsak fordi man kan utnytte tilgjengelig teori og programvare for å løse hver undermodell svært effektivt. Ulempen er at man kan ende opp med løsningsalgoritmer for den sammenkoblede modellen som er trege, eller ikke kommer frem til noen løsning i det hele tatt. I denne avhandlingen har tre forskjellige metoder for å forbedre splittemetoder blitt utviklet for tre forskjellige sammenkoblede modeller. Den første modellen beskriver flyt gjennom deformerbart porøst medium og er kjent som Biot ligningene. For å anvende en splittemetode på denne modellen har et stabiliseringsledd blitt tilført. Dette sikrer at metoden konvergerer (kommer frem til en løsning), men dersom man ikke skalerer stabiliseringsleddet riktig kan det ta veldig lang tid. Derfor har et intervall hvor den optimale skaleringen av stabiliseringsleddet befinner seg blitt identifisert, og utfra dette presenteres det en måte å praktisk velge den riktige skaleringen på. Den andre modellen er en fasefeltmodell for sprekkpropagering. Denne modellen løses vanligvis med en splittemetode som er veldig treg, men konvergent. For å forbedre dette har en ny akselerasjonsmetode har blitt utviklet. Denne anvendes som et postprosesseringssteg til den klassiske splittemetoden, og utnytter både overrelaksering og Anderson akselerasjon. Disse to forskjellige akselerasjonsmetodene har kompatible styrker i at overrelaksering akselererer når man er langt fra løsningen (som er tilfellet når sprekken propagerer), og Anderson akselerasjon fungerer bra når man er nærme løsningen. For å veksle mellom de to metodene har et kriterium basert på residualfeilen blitt brukt. Resultatet er en pålitelig akselerasjonsmetode som alltid akselererer og ofte er svært effektiv. Det siste modellen kalles Cahn-Larché ligningene og er også en fasefeltmodell, men denne beskriver elastisitet i et medium bestående av to elastiske materialer som kan bevege seg basert på overflatespenningen mellom dem. Dette problemet er spesielt utfordrende å løse da det verken er lineært eller konvekst. For å håndtere dette har en ny måte å behandle tidsavhengigheten til det underliggende koblede problemet på blitt utviklet. Dette leder til et diskret system som er ekvivalent med et konvekst minimeringsproblem, som derfor er velegnet til å løses med de fleste numeriske optimeringsmetoder, også splittemetoder. Den nye modellen som har blitt utviklet er en utvidelse av Cahn-Larché ligningene og har fått navnet Cahn-Hilliard-Biot. Dette er fordi ligningene utgjør en fasefelt modell som beskriver flyt i et deformerbart porøst medium med to poroelastiske materialer. Disse kan forflytte seg basert på overflatespenning, elastisk spenning, og poretrykk, og det er tenkt at modellen kan anvendes i forbindelse med kreftsvulstmodellering.There are many applications where the study of coupled physical processes is of great importance. These range from the life sciences with flow in deformable human tissue to structural engineering with fracture propagation in elastic solids. In this doctoral dissertation, there is a twofold focus on coupled problems. Firstly, robust and efficient solution strategies, with a focus on iterative decoupling methods, have been applied to several coupled systems of equations. Secondly, a new thermodynamically consistent coupled system of equations is proposed. Solution strategies are developed for three different coupled problems; the quasi-static linearized Biot equations that couples flow through porous materials and elastic deformation of the solid medium, variational phase-field models for brittle fracture that couple a phase-field equation for fracture evolution with linearized elasticity, and the Cahn-Larché equations that model elastic effects in a two-phase elastic material and couples an extended Cahn-Hilliard phase-field equation and linearized elasticity. Finally, the new system of equations that is proposed models flow through a two-phase deformable porous material where the solid phase evolution is governed by interfacial forces as well as effects from both the fluid and elastic properties of the material. In the work that concerns the quasi-static linearized Biot equations, the focus is on the fixed-stress splitting scheme, which is a popular method for sequentially solving the flow and elasticity subsystems of the full model. Using such a method is beneficial as it allows for the use of readily available solvers for the subproblems; however, a stabilizing term is required for the scheme to converge. It is well known that the convergence properties of the method strongly depend on how this term is chosen, and here, the optimal choice of it is addressed both theoretically and practically. An interval where the optimal stabilization parameter lies is provided, depending on the material parameters. In addition, two different ways of optimizing the parameter are proposed. The first is a brute-force method that relies on the mesh independence of the scheme's optimal stabilization parameter, and the second is valid for low-permeable media and utilizes an equivalence between the fixed-stress splitting scheme and the modified Richardson iteration. Regarding the variational phase-field model for brittle fracture propagation, the focus is on improving the convergence properties of the most commonly used solution strategy with an acceleration method. This solution strategy relies on a staggered scheme that alternates between solving the elasticity and phase-field subproblems in an iterative way. This is known to be a robust method compared to the monolithic Newton method. However, the staggered scheme often requires many iterations to converge to satisfactory precision. The contribution of this work is to accelerate the solver through a new acceleration method that combines Anderson acceleration and over-relaxation, dynamically switching back and forth between them depending on a criterion that takes the residual evolution into account. The acceleration scheme takes advantage of the strengths of both Anderson acceleration and over-relaxation, and the fact that they are complementary when applied to this problem, resulting in a significant speed-up of the convergence. Moreover, the method is applied as a post-processing technique to the increments of the solver, and can thus be implemented with minor modifications to readily available software. The final contribution toward solution strategies for coupled problems focuses on the Cahn-Larché equations. This is a model for linearized elasticity in a medium with two elastic phases that evolve with respect to interfacial forces and elastic effects. The system couples linearized elasticity and an extended Cahn-Hilliard phase-field equation. There are several challenging features with regards to solution strategies for this system including nonlinear coupling terms, and the fourth-order term that comes from the Cahn-Hilliard subsystem. Moreover, the system is nonlinear and non-convex with respect to both the phase-field and the displacement. In this work, a new semi-implicit time discretization that extends the standard convex-concave splitting method applied to the double-well potential from the Cahn-Hilliard subsystem is proposed. The extension includes special treatment for the elastic energy, and it is shown that the resulting discrete system is equivalent to a convex minimization problem. Furthermore, an alternating minimization solver is proposed for the fully discrete system, together with a convergence proof that includes convergence rates. Through numerical experiments, it becomes evident that the newly proposed discretization method leads to a system that is far better conditioned for linearization methods than standard time discretizations. Finally, a new model for flow through a two-phase deformable porous material is proposed. The two poroelastic phases have distinct material properties, and their interface evolves according to a generalized Ginzburg–Landau energy functional. As a result, a model that extends the Cahn-Larché equations to poroelasticity is proposed, and essential coupling terms for several applications are highlighted. These include solid tumor growth, biogrout, and wood growth. Moreover, the coupled set of equations is shown to be a generalized gradient flow. This implies that the system is thermodynamically consistent and makes a toolbox of analysis and solvers available for further study of the model.Doktorgradsavhandlin

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Um modelo numérico para a análise de problemas de interação fluido-estrutura envolvendo escoamentos de superfície livre

O presente trabalho tem por objetivo desenvolver ferramentas numéricas para a resolução de problemas de Interação Fluido-Estrutura (IFE) envolvendo corpos flutuantes sujeitos à ação de escoamentos multifásicos com superfície livre, onde a estrutura pode ou não estar ancorada através de cabos de amarração. Para o tratamento numérico de fluidos em escoamento incompressível, as equações de Navier-Stokes e da continuidade são discretizadas empregando-se uma versão semi-implícita do método CBS (Characteristic-Based Split) no contexto do Método dos Elementos Finitos, onde elementos tetraédricos lineares são utilizados. A turbulência é analisada através da Simulação de Grandes Escalas (LES – Large Eddy Simulation), utilizando os modelos sub-malha clássico e dinâmico de Smagorinsky, e para o tratamento de escoamentos multifásicos com superfície livre, utiliza-se o método Level Set. Na presença de estruturas móveis, as equações do escoamento são descritas através de uma formulação arbitrária lagrangiana-euleriana (ALE) e um esquema numérico de movimento de malha é adotado. A estrutura é tratada através de uma abordagem de corpo rígido tridimensional e o cabo de amarração através de um modelo elástico com não linearidade geométrica e discretização pelo Método de Elementos Finitos Posicional (NPFEM – Nodal Position Finite Element Method). O sistema de equações de movimento pode ser discretizado temporalmente através dos métodos implícitos de Newmark e a-Generalizado ou através dos métodos explícitos de Euler e Runge-Kutta. Para problemas de IFE, um esquema particionado de acoplamento forte é utilizado levando-se em conta os acoplamentos fluidoestrutura e cabo-estrutura. Os algoritmos que compõem o código numérico são primeiramente verificados usando-se problemas clássicos da Dinâmica de Fluidos Computacional e de IFE, além de aplicações envolvendo a análise dinâmica de cabos. Finalmente, problemas envolvendo corpos flutuantes com e sem ancoragem são simulados para demonstrar a aplicabilidade e a precisão do modelo numérico proposto.The present work proposes the development of numerical tools capable of solving Fluid- Structure Interaction (FSI) problems involving rigid floating bodies subjected to the action of multiphase free-surface flows, where the structure may or may not be anchored through mooring cables. For the numerical treatment of the incompressible fluid flows, the Navier- Stokes and continuity equations are discretized using a semi-implicit version of the CBS (Characteristic-Based Split) method in the context of the Finite Element Method, using linear tetrahedral elements. Turbulence is analyzed using Large Eddy Simulation (LES) with the Smagorinsky's classic and dynamic sub-grid models. For the treatment of multiphase freesurface flows, the Level Set method is used. In the presence of moving structures, the flow equations are described through an arbitrary lagrangean-eulerian (ALE) formulation and a numerical scheme for mesh movement is adopted. The structure is treated using a threedimensional rigid body approach and the mooring cable is modeled using an elastic material with geometric nonlinearity and the Nodal Position Finite Element Method (NPFEM). The system of equations of motion may be discretized in time using the implicit Newmark and a- Generalized methods or the explicit Euler and Runge-Kutta methods. For FSI problems, a partitioned strong coupling scheme is adopted, taking in consideration the fluid-structure and cable-structure couplings. The algorithms constituting the numerical code are first verified using classical problems of Computational Fluid Dynamics and FSI, in addition to applications involving the dynamic analysis of cables. Finally, problems involving floating bodies with and without anchoring are simulated to demonstrate the applicability and accuracy of the proposed numerical model