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  • 1. Guermond, Jean-Luc
    et al.
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Popov, Bojan
    Implementation of the entropy viscosity method2011Report (Other academic)
  • 2.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    de Abreu, Rodrigo Vilela
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Degirmenci, Niyazi Cem
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Müller, Kaspar
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Spühler, Jeannette Hiromi
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Unicorn: Parallel adaptive finite element simulation of turbulent flow and fluid-structure interaction for deforming domains and complex geometry2013In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 80, no SI, p. 310-319Article in journal (Refereed)
    Abstract [en]

    We present a framework for adaptive finite element computation of turbulent flow and fluid structure interaction, with focus on general algorithms that allow for complex geometry and deforming domains. We give basic models and finite element discretization methods, adaptive algorithms and strategies for efficient parallel implementation. To illustrate the capabilities of the computational framework, we show a number of application examples from aerodynamics, aero-acoustics, biomedicine and geophysics. The computational tools are free to download open source as Unicorn, and as a high performance branch of the finite element problem solving environment DOLFIN, both part of the FEniCS project.

  • 3.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Degirmenci, Niyazi Cem
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Unicorn: a unified continuum mechanics solver; in automated solution pf differential equations by the finite element method2011In: Automated Solution of Differential Equations by the Finite Element Method, Springer Berlin/Heidelberg, 2011Chapter in book (Refereed)
  • 4.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Jansson, Johan
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A General Galerkin Finite Element Method for the Compressible Euler Equations2008In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197Article in journal (Refereed)
    Abstract [en]

    In this paper we present a General Galerkin (G2) method for the compressible Euler equations, including turbulent ow. The G2 method presented in this paper is a nite element method with linear approximation in space and time, with componentwise stabilization in the form  of streamline diusion and shock-capturing modi cations. The method conserves mass, momentum  and energy, and we prove an a posteriori version of the 2nd Law of thermodynamics for the method.  We illustrate the method for a laminar shock tube problem for which there exists an exact analytical  solution, and also for a turbulent flow problem

  • 5.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Vilela de Abreu, Rodrigo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Degirmenci, Niyazi Cem
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Müller, Kaspar
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Spühler, Jeannette Hiromi
    Unicorn: Parallel adaptive finite element simulation of turbulent flow and fluid-structure interaction for deforming domains and complex geometry2011Report (Other academic)
    Abstract [en]

    We present a framework for adaptive finite element computation of turbulent flow and fluid-structure interaction, with focus on general algorithms that allow for complex geometry and deforming domains. We give basic models and finite element discretization methods, adaptive algorithms and strategies for e cient parallel implementation. To illustrate the capabilities of the computational framework, we show a number of application examples from aerodynamics, aero-acoustics, biomedicine and geophysics. The computational tools are free to download open source as Unicorn, and as a high performance branch of the finite element problem solving environment DOLFIN, both part of the FEniCS project

  • 6.
    Jansson, Niclas
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Adaptive simulation of turbulent flow past a full car model2011In: State of the Practice Reports, SC'11, 2011Conference paper (Refereed)
    Abstract [en]

    The massive computational cost for resolving all turbulent scales makes a direct numerical simulation of the underlying Navier-Stokes equations impossible in most engineering applications. We present recent advances in parallel adaptive finite element methodology that enable us to efficiently compute time resolved approximations for complex geometries with error control. In this paper we present a LES simulation of turbulent flow past a full car model, where we adaptively refine the unstructured mesh to minimize the error in drag prediction. The simulation was partly carried out on the new Cray XE6 at PDC/KTH where the solver shows near optimal strong and weak scaling for the entire adaptive process.

  • 7.
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Adaptive Algorithms and High Order Stabilization for Finite Element Computation of Turbulent Compressible Flow2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This work develops finite element methods with high order stabilization, and robust and efficient adaptive algorithms for Large Eddy Simulation of turbulent compressible flows.

    The equations are approximated by continuous piecewise linear functions in space, and the time discretization is done in implicit/explicit fashion: the second order Crank-Nicholson method and third/fourth order explicit Runge-Kutta methods. The full residual of the system and the entropy residual, are used in the construction of the stabilization terms. These methods are consistent for the exact solution, conserves all the quantities, such as mass, momentum and energy, is accurate and very simple to implement. We prove convergence of the method for scalar conservation laws in the case of an implicit scheme. The convergence analysis is based on showing that the approximation is uniformly bounded, weakly consistent with all entropy inequalities, and strongly consistent with the initial data. The convergence of the explicit schemes is tested in numerical examples in 1D, 2D and 3D.

    To resolve the small scales of the flow, such as turbulence fluctuations, shocks, discontinuities and acoustic waves, the simulation needs very fine meshes. In this thesis, a robust adjoint based adaptive algorithm is developed for the time-dependent compressible Euler/Navier-Stokes equations. The adaptation is driven by the minimization of the error in quantities of interest such as stresses, drag and lift forces, or the mean value of some quantity.

    The implementation and analysis are validated in computational tests, both with respect to the stabilization and the duality based adaptation.

  • 8.
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    An adaptive finite element method for the compressible Euler equations2009Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This work develops a stabilized finite element method for the compressible Euler equations and proves an a posteriori error estimate for the approximated solution. The equations are approximated by the cG(1)cG(1) finite element method with continuous piecewise linear functions in space and time. cG(1)cG(1) gives a second order accuracy in space, and corresponds to a Crank-Nicholson type of discretization in time, resulting in second order accuracy in space, without a stabilization term.

    The method is stabilized by componentwise weighted least squares stabilization of the convection terms, and residual based shock capturing. This choice of stabilization gives a symmetric stabilization matrix in the discrete system. The method is successfully implemented for a number of benchmark problems in 1D, 2D and 3D. We observe that cG(1)cG(1) with the above choice of stabilization is robust and converges to an accurate solution with residual based adaptive mesh refinement.

    We then extend the General Galerkin framework from incompressible to compressible flow, with duality based a posteriori error estimation of some quantity of interest. The quantities of interest can be stresses, strains, drag and lift forces, surface forces or a mean value of some quantity. In this work we prove a duality based a posteriori error estimate for the compressible equations, as an extension of the earlier work for incompressible flow [25].

    The implementation and analysis are validated in computational tests both with respect to the stabilization and the duality based adaptation

     

     

     

  • 9.
    Nazarov, Murtazo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Convergence of a residual based artificial viscosity finite element method2011Report (Other academic)
  • 10.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Guermond, Jean-Luc
    Popov, Bojan
    A posteriori error estimation for the compressible Euler equations using entropy viscosity2011Report (Other academic)
  • 11.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    An adaptive finite element method for inviscid compressible flow2010In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 64, no 10-12, p. 1102-1128Article in journal (Refereed)
    Abstract [en]

    We present an adaptive finite element method for the compressible Euler equations, based on a posteriori error estimation of a quantity of interest in terms of a dual problem for the linearized equations. Continuous piecewise linear approximation is used in space and time, with componentwise weighted least-squares stabilization of convection terms and residual-based shock-capturing. The adaptive algorithm is demonstrated numerically for the quantity of interest being the drag force on a body.

  • 12.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    An adaptive finite element method for the compressible Euler equations2010In: INT J NUMER METHOD FLUID, 2010, Vol. 64, no 10-12, p. 1102-1128Conference paper (Refereed)
    Abstract [en]

    We present an adaptive finite element method for the compressible Euler equations, based on a posteriori error estimation of a quantity of interest in terms of a dual problem for the linearized equations. Continuous piecewise linear approximation is used in space and time, with componentwise weighted least-squares stabilization of convection terms and residual-based shock-capturing. The adaptive algorithm is demonstrated numerically for the quantity of interest being the drag force on a body.

  • 13.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    On the stability of the dual problem for high Reynolds number flow past a circular cylinder in two dimensions2011Report (Other academic)
  • 14.
    Nazarov, Murtazo
    et al.
    Texas A and M University, United States.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    On the stability of the dual problem for high Reynolds number flow past a circular cylinder in two dimensions2012In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 34, no 4, p. A1905-A1924Article in journal (Refereed)
    Abstract [en]

    In this paper we present a computational study of the stability of time dependent dual problems for compressible flow at high Reynolds numbers in two dimensions. The dual problem measures the sensitivity of an output functional with respect to numerical errors and is a key part of goal oriented a posteriori error estimation. Our investigation shows that the dual problem associated with the computation of the drag force for the compressible Euler/Navier-Stokes equations, which are approximated numerically using different temporal discretization and stabilization techniques, is unstable and exhibits blow-up for several Mach regimes considered in this paper.

  • 15.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Residual based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods2011Report (Other academic)
1 - 15 of 15
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