Development of a Balanced Adaptive Time-Stepping Strategy Based on an Implicit JFNK-DG Compressible Flow Solver

Pan, Yu; Yan, Zhenguo; Peiró, Joaquim; Sherwin, Spencer J.

doi:10.1007/s42967-021-00138-1

Cited by 8 publications

(3 citation statements)

References 29 publications

(78 reference statements)

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“…Stable implicit methods exist for virtually any order and possess the advantage of choosing the time step only according to accuracy or physical criteria 9 . Several authors used Diagonally Implicit Runge‐Kutta (DIRK) methods for simulation of compressible flows, for example, References 10‐15. The application of fully implicit Runge‐Kutta (IRK) methods to incompressible flows is more complicated due to the quasi‐static nature of the continuity equation, but was investigated in References 14,16‐18.…”

Section: Introductionmentioning

confidence: 99%

Assessment of high‐order IMEX methods for incompressible flow

Montadhar

Grotteschi

Stiller

2023

Numerical Methods in Fluids

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This paper investigates the competitiveness of semi-implicit Runge-Kutta (RK) and spectral deferred correction (SDC) time-integration methods up to order six for incompressible Navier-Stokes problems in conjunction with a high-order discontinuous Galerkin method for space discretization. It is proposed to harness the implicit and explicit RK parts as a partitioned scheme, which provides a natural basis for the underlying projection scheme and yields a straight-forward approach for accommodating nonlinear viscosity. Numerical experiments on laminar flow, variable viscosity and transition to turbulence are carried out to assess accuracy, convergence and computational efficiency. Although the methods of order 3 or higher are susceptible to order reduction due to time-dependent boundary conditions, two third-order RK methods are identified that perform well in all test cases and clearly surpass all second-order schemes including the popular extrapolated backward difference method. The considered SDC methods are more accurate than the RK methods, but become competitive only for relative errors smaller than ca 10 −5 .

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Section: Introductionmentioning

confidence: 99%

Assessment of high‐order IMEX methods for incompressible flow

Montadhar

Grotteschi

Stiller

2023

Numerical Methods in Fluids

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“…Several authors used Diagonally Implicit Runge-Kutta (DIRK) methods for simulation of compressible flows, e.g. [4,26,42,43,45,56]. The application of implicit Runge-Kutta (IRK) methods to incompressible flows is more complicated due to the quasi-static nature of the continuity equation, but was investigated in [4,24,40].…”

Section: Introductionmentioning

confidence: 99%

Assessment of high-order IMEX methods for incompressible flow

Montadhar¹,

Grotteschi²,

Stiller³

2021

Preprint

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This paper investigates the competitiveness of semi-implicit Runge-Kutta (RK) and spectral deferred correction (SDC) time-integration methods up to order six for incompressible Navier-Stokes problems in conjunction with a high-order discontinuous Galerkin method for space discretization. It is proposed to harness the implicit and explicit RK parts as a partitioned scheme, which provides a natural basis for the underlying projection scheme and yields a straight-forward approach for accommodating nonlinear viscosity. Numerical experiments on laminar flow, variable viscosity and transition to turbulence are carried out to assess accuracy, convergence and computational efficiency. Although the methods of order 3 or higher are susceptible to order reduction due to time-dependent boundary conditions, two thirdorder RK methods are identified that perform well in all test cases and clearly surpass all second-order schemes including the popular extrapolated backward difference method. The considered SDC methods are more accurate than the RK methods, but become competitive only for relative errors smaller than ca 10 −5 .

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“…Due to the wide range of scales that the compressible Navier-Stokes problem expands, the selection of the time step size is crucial. Thus, we consider that the implementation of adaptive time stepping techniques would be a very important feature to add to the present code enabling the efficient simulation of practical applications (see e.g., [179][180][181]). In fact, this is a research line of great interest in our group that could lead to the development of a new thesis.…”

Section: Afterwordmentioning

confidence: 99%

Development of fractional step methods for compressible flow solvers using variational multi-scale finite element formulations

Parada Bustelo

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(English) This thesis deals with finite element methods to solve compressible flow problems, an important branch of Computational Fluid Dynamics (CFD) whose applications are widespread in many areas of engineering and science. In spite of the increasing amount of computational resources made available for the scientific and engineering research communities, the numerical simulation of complex compressible phenomena in many practical applications is still a challenge. These type of flow problems are extremely demanding in what concerns numerical computations and memory requirements. In particular, in this thesis we investigate the possibility to solve the underlying algebraic systems in a decoupled manner, a technique usually called fractional step or segregation method. Although segregation techniques have been broadly studied and analyzed for the incompressible Navier-Stokes equations, allowing for the separate resolution of velocity and pressure unkonwns, much less has been explored for compressible problems. The interest on this type of technique not only comes from the fact that it permits a segregated calculation of the problem unkonwns (usually leading to better conditioned systems) but from the associated reduction of the computational cost. We study three different problems inside the compressible CFD research branch in separated chapters: the isentropic Navier-Stokes equations, the Navier-Stokes problem written in primitive variables (velocity, pressure and temperature), and the navier-Stokes problem written in the classical formulation with conservative variables (momentum, density, total energy). For each of these problems, first we propose a finite element stabilized formulation framed within the Variational MultiScale concept, which allows to use equal interpolation spaces for all the variables in play. Second, and once space and time discretizations are selected, we derive fractional step methods up to second order in time. Finally, all the schemes are implemented in a parallel multiphysics code and representative simulations are carried out in order to analyze the performance of the proposed techniques. (Español) Esta tesis se centra en la aplicación del método de elementos finitos a problemas de flujo compresible, unas de las ramas más importantes dentro de la mecánica de fluidos computacional (CFD, por sus siglas en inglés), y cuya aplicación es amplia en distintas áreas de ciencia e ingeniería. A pesar del aumento de los recursos computacionales que se ponen a disposición de la comunidad científica, la solución numérica de problemas complejos de flujo compresible para distintas aplicaciones prácticas es aún un reto. Este tipo de problemas de flujo son extremadamente exigentes en lo que se refiere al cálculo numérico y los requisitos de memoria computacionales. En particular, en esta tesis se estudia la posibilidad de resolver los sistemas algebraicos que subyacen tras la aplicación del método de elementos finitos de una forma desacoplada, una técnica que usualmente se denomina de paso fraccionado o método de segregación. Aunque las técnicas de segregación han sido ampliamente estudiadas y analizadas para el problema incompresible de Navier-Stokes, lo que permite un cálculo separado de las variables velocidad y presión, poco se ha explorado su aplicación a problemas de flujo compresible. El interés en este tipo de técnicas radica no solo en el hecho de que permite un cálculo segregado de las incógnitas del problema (generalmente dando lugar además a sistemas algebraicos mejor condicionados), sino también en la reducción de coste computacional que ofrecen. Se estudian tres problemas distintos dentro de la rama de investigación en CFD de flujos compresibles: las ecuaciones isentrópicas de Navier-Stokes, el problema compresible de Navier-Stokes escrito en variables primitivas (velocidad, presión y temperatura) y el problema compresible de Navier-Stokes planteado de manera clásica en variables conservativas (momento, densidad y energía total). Para cada uno de estos casos, primero se propone una formulación de elementos finitos, estabilizada bajo el marco de trabajo de las multiescalas variacionales (VMS, por sus siglas en inglés), lo que en la práctica permite utilizar la misma interpolación para las variables del problema. En segundo lugar, y una vez las discretizaciones en tiempo y espacio han sido seleccionadas, se proponen métodos de paso fraccionado para cada problema de hasta segundo orden en tiempo. Finalmente, todos los algoritmos se implementan en una plataforma de código paralelo para problemas multifísicos y se llevan a cabo simulaciones representativas con el fin de analizar el rendimiento de las técnicas propuestas.

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Development of a Balanced Adaptive Time-Stepping Strategy Based on an Implicit JFNK-DG Compressible Flow Solver

Cited by 8 publications

References 29 publications

Assessment of high‐order IMEX methods for incompressible flow

Assessment of high‐order IMEX methods for incompressible flow

Assessment of high-order IMEX methods for incompressible flow

Development of fractional step methods for compressible flow solvers using variational multi-scale finite element formulations

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