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| 2. |
- Hoffman, Johan, 1974, et al.
(författare)
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Mathematics and Computation
- 2004
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Ingår i: Stockholm Intelligencer: Fourth European Congress of Mathematics.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 3. |
- Hoffman, Johan, et al.
(författare)
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Subgrid modeling for convection-diffusion-reaction in one space dimension using a Haar Multiresolution analysis
- 2005
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 194:1, s. 19-44
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we propose and study a subgrid model for linear convection-diffusion-reaction equations with fractal rough coefficients. The subgrid model is based on scale extrapolation of a modeling residual from coarser scales using a computed solution on a finest scale as reference. We show in experiments that a solution with subgrid model on a scale h in most cases corresponds to a solution without subgrid model on a scale less than h/4. We also present error estimates for the modeling error in terms of modeling residuals.
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| 4. |
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| 5. |
- Balmus, Maximilian, et al.
(författare)
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A partition of unity approach to fluid mechanics and fluid-structure interaction
- 2020
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : ELSEVIER SCIENCE SA. - 0045-7825 .- 1879-2138. ; 362
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Tidskriftsartikel (refereegranskat)abstract
- For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains a computationally expensive endeavour which continues to drive interest in the development of novel approaches. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of 2D flow past an elastic beam simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.
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| 6. |
- Balmus, Maximilian, et al.
(författare)
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A stabilized multidomain partition of unity approach to solving incompressible viscous flow
- 2022
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 392
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Tidskriftsartikel (refereegranskat)abstract
- In this work we propose a new stabilized approach for solving the incompressible Navier-Stokes equations on fixed overlapping grids. This new approach is based on the partition of unity finite element method, which defines the solution fields as weighted sums of local fields, supported by the different grids. Here, the discrete weak formulation of the problem is re-set in cG(1)cG(1) stabilized form, which has the dual benefit of lowering grid resolution requirements for convection dominated flows and allowing for the use of velocity and pressure discretizations which do not satisfy the inf-sup condition. Additionally, we provide an outline of our implementation within an existing distributed parallel application and identify four key options to improve the code efficiency namely: the use of cache to store mapped quadrature points and basis function gradients, the intersection volume splitting algorithm, the use of lower order quadrature schemes, and tuning the partition weight associated with the interface elements. The new method is shown to have comparable accuracy to the single mesh boundary-fitted version of the same stabilized solver based on three transient flow tests including both 2D and 3D settings, as well as low and moderate Reynolds number flow conditions. Moreover, we demonstrate how the four implementation options have a synergistic effect lowering the residual assembly time by an order of magnitude compared to a naive implementation, and showing good load balancing properties.
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| 7. |
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| 8. |
- Degirmenci, Niyazi Cem, 1982-
(författare)
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Adaptive Finite Element Methods for Fluid Structure Interaction Problems with Applications to Human Phonation
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This work presents a unified framework for numerical solution of Fluid Structure Interaction (FSI) and acoustics problems with focus on human phonation. The Finite Element Method is employed for numerical investigation of partial differential equations that model conservation of momentum and mass. Since the resulting system of equations is very large, an efficient open source high performance implementation is constructed and provided. In order to gain accuracy for the numerical solutions, an adaptive mesh refinement strategy is employed which reduces the computational cost in comparison to a uniform refinement. Adaptive refinement of the mesh relies on computable error indicators which appear as a combination of a computable residual and the solution of a so-called dual problem acting as weights on computed residuals. The first main achievement of this thesis is to apply this strategy to numerical simulations of a benchmark problem for FSI. This FSI model is further extended for contact handling and applied to a realistic vocal folds geometry where the glottic wave formation was captured in the numerical simulations. This is the second achievement in the presented work. The FSI model is further coupled to an acoustics model through an acoustic analogy, for vocal folds with flow induced oscillations for a domain constructed to create the vowel /i/. The comparisons of the obtained pressure signal at specified points with respect to results from literature for the same vowel is reported, which is the final main result presented.
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| 9. |
- Hoffman, Johan, et al.
(författare)
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A computational study of turbulent flow separation for a circular cylinder using skin friction boundary conditions
- 2011
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Ingår i: Quality And Reliability Of Large-Eddy Simulations II. - Dordrecht : Springer Netherlands. - 9789400702301 ; , s. 57-68
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Konferensbidrag (refereegranskat)abstract
- In this paper we present a computational study of turbulent flow separation for a circular cylinder at high Reynolds numbers. We use a stabilized finite element method together with skin friction boundary conditions, where we study flow separation with respect to the decrease of a friction parameter. In particular, we consider the case of zero friction corresponding to pure slip boundary conditions, for which we observe an inviscid separation mechanism of large scale streamwise vortices, identified in our earlier work. We compare our computational results to experiments for very high Reynolds numbers. In particular, we connect the pattern of streamwise vorticity in our computations to experimental findings of spanwise 3d cell structures reported in the literature.
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| 10. |
- Hoffman, Johan, et al.
(författare)
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A new approach to computational turbulence modeling
- 2006
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 195:23-24, s. 2865-2880
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Tidskriftsartikel (refereegranskat)abstract
- We present a new approach to computational fluid dynamics (CFD) using adaptive stabilized Galerkin finite element methods with duality based a posteriori error control for chosen output quantities of interest. We address the basic question of computability in CFD: For a given flow, what quantity is computable to what tolerance to what cost? We focus on incompressible Newtonian flow with medium to large Reynolds numbers involving both laminar and turbulent flow features. We estimate a posteriori the output of the computed solution with the output based on the exact solution to the Navier–Stokes equations, thus circumventing introducing and modeling Reynolds stresses in averaged Navier–Stokes equations. Our basic tool is a representation formula for the error in the quantity of interest in terms of a space–time integral of the residual of a computed solution multiplied by weights related to derivatives of the solution of an associated dual problem with data connected to the output. We use the error representation formula to derive an a posteriori error estimate combining residuals with computed dual weights, which is used for mesh adaptivity in space–time with the objective of satisfying a given error tolerance with minimal computational effort. We show in a concrete example that outputs such as a mean value in time of drag of a turbulent flow around a bluff body are computable on a PC with a tolerance of a few percent using a few hundred thousand mesh points in space. We refer to our methodology as adaptive DNS/LES, where automatically by adaptivity certain features of the flow are resolved in a direct numerical simulation (DNS), while certain other small scale turbulent features are left unresolved in a large eddy simulation (LES). The stabilization of the Galerkin method giving a weighted least square control of the residual acts as the subgrid model in the LES. The a posteriori error estimate takes into account both the error from discretization and the error from the subgrid model. We pay particular attention to the stability of the dual solution from (i) perturbations replacing the exact convection velocity by a computed velocity, and (ii) computational solution of the dual problem, which are the crucial aspects entering by avoiding using averaged Navier–Stokes equations including Reynolds stresses. A crucial observation is that the contribution from subgrid modeling in the a posteriori error estimation is small, making it possible to simulate aspects of turbulent flow without accurate modeling of Reynolds stresses.
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