| 1. |
- Eliasson, Peter, et al.
(författare)
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A global time integration approach for realistic unsteady flow computations
- 2016
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Konferensbidrag (refereegranskat)abstract
- A novel time integration approach is explored for unsteady flow computations. It is a multi-block formulation in time where one solves for all time levels within a block simultaneously. The time discretization within a block is based on the summation-by-parts (SBP) technique in time combined with the simultaneous-approximation-term (SAT) technique for imposing the initial condition. The approach is implicit, unconditionally stable and can be made high order accurate in time. The implicit system is solved by a dual time stepping technique. The technique has been implemented in a flow solver for unstructured grids and applied to an unsteady flow problem with vortex shedding over a cylinder. Four time integration approaches being 2nd to 5th order accurate in time are evaluated and compared to the conventional 2nd order backward difference (BDF2) method and a 4th order diagonally implicit Runge-Kutta scheme (ESDIRK64). The obtained orders of accuracy are higher than expected and correspond to the accuracy in the interior of the blocks, up to 8th order accuracy is obtained. The influence on the accuracy from the size of the time blocks is small. Smaller blocks are computationally more efficient though, and the efficiency increases with increased accuracy of the SBP operator and reduced size of time steps. The most accurate scheme, with a small time step and block size, is approximately as efficient as the ESDIRK64 scheme. There is a significant potential for improvements ranging from convergence acceleration techniques in dual time, alternative initialization of time blocks, and by introducing smaller time blocks based on alternative SBP operators.
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| 2. |
- Hosseinzadeh, Griffin, et al.
(författare)
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Weak Mass Loss from the Red Supergiant Progenitor of the Type II SN 2021yja
- 2022
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Ingår i: Astrophysical Journal. - : American Astronomical Society. - 0004-637X .- 1538-4357. ; 935:1
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Tidskriftsartikel (refereegranskat)abstract
- We present high-cadence optical, ultraviolet (UV), and near-infrared data of the nearby (D approximate to 23 Mpc) Type II supernova (SN) 2021yja. Many Type II SNe show signs of interaction with circumstellar material (CSM) during the first few days after explosion, implying that their red supergiant (RSG) progenitors experience episodic or eruptive mass loss. However, because it is difficult to discover SNe early, the diversity of CSM configurations in RSGs has not been fully mapped. SN 2021yja, first detected within approximate to 5.4 hours of explosion, shows some signatures of CSM interaction (high UV luminosity and radio and x-ray emission) but without the narrow emission lines or early light-curve peak that can accompany CSM. Here we analyze the densely sampled early light curve and spectral series of this nearby SN to infer the properties of its progenitor and CSM. We find that the most likely progenitor was an RSG with an extended envelope, encompassed by low-density CSM. We also present archival Hubble Space Telescope imaging of the host galaxy of SN 2021yja, which allows us to place a stringent upper limit of less than or similar to 9 M-circle dot; on the progenitor mass. However, this is in tension with some aspects of the SN evolution, which point to a more massive progenitor. Our analysis highlights the need to consider progenitor structure when making inferences about CSM properties, and that a comprehensive view of CSM tracers should be made to give a fuller view of the last years of RSG evolution.
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| 3. |
- Linders, Viktor, 1988-, et al.
(författare)
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On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-By-Parts Form
- 2017
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we generalise results regarding the order of accuracy of finite difference operators on Summation-By-Parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. Additionally, we prove that if the order of accuracy in the interior is precisely twice that of the boundary, then the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid point distribution near the domain boundaries.
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| 4. |
- Linders, Viktor, 1988-, et al.
(författare)
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On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-by-Parts Form
- 2018
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1429 .- 1095-7170. ; 56:2, s. 1048-1063
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we generalize results regarding the order of accuracy of finite difference operators on summation-by-parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. Additionally, we prove that if the order of accuracy in the interior is precisely twice that of the boundary, then the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid point distribution near the domain boundaries.
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| 5. |
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| 6. |
- Lundquist, Tomas, et al.
(författare)
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A hybrid framework for coupling arbitrary summation-by-parts schemes on general meshes
- 2018
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Ingår i: Journal of Computational Physics. - : Springer. - 0021-9991 .- 1090-2716. ; 362, s. 49-68
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Tidskriftsartikel (refereegranskat)abstract
- We develop a general interface procedure to couple both structured and unstructured parts of a hybrid mesh in a non-collocated, multi-block fashion. The target is to gain optimal computational efficiency in fluid dynamics simulations involving complex geometries. While guaranteeing stability, the proposed procedure is optimized for accuracy and requires minimal algorithmic modifications to already existing schemes. Initial numerical investigations confirm considerable efficiency gains compared to non-hybrid calculations of up to an order of magnitude.
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| 7. |
- Lundquist, Tomas, 1986-, et al.
(författare)
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A Method-of-Lines Framework for Energy Stable Arbitrary Lagrangian–Eulerian Methods
- 2023
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1429 .- 1095-7170. ; 61:5, s. 2327-2351
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Tidskriftsartikel (refereegranskat)abstract
- We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and energy stable discretizations from stationary domains to the general case, including arbitrary mesh motion. In particular, we show that an energy estimate derived in the physical coordinate system is equivalent to a semi-bounded property with respect to a stationary reference domain. The continuous analysis leading up to this result is based on a skew-symmetric splitting of the material time derivative and thus relies on the property of integration-by-parts. Following this, a mimetic energy stable arbitrary Lagrangian–Eulerian framework for semi-discretization is formulated, based on approximating the material time derivative in a way consistent with discrete summation-by-parts. Thanks to the semi-bounded property, a method-of-lines approach using standard explicit or implicit time integration schemes can be applied to march the system forward in time. The same type of stability arguments as for the corresponding stationary domain problem applies, without regard to additional properties such as discrete geometric conservation. As an additional bonus we demonstrate that discrete geometric conservation, in the sense of exact free-stream preservation, can still be achieved in an automatic way with the new framework. However, we stress that this is not necessary for stability.
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| 8. |
- Lundquist, Tomas, 1986-, et al.
(författare)
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A multi-domain summation by-parts formulation for complex geometries
- 2021
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We combine existing discretization methods to obtain a simplified numerical formulation of partial derivative equations posed on multi-block/element domains. The interfaces (conforming or non-conforming) between blocks are treated with inner-product-preserving interpolation operators. The result is a single set of high-order multi-block summation-by-parts operators that encapsulates both the metric terms and the interface treatments. This enables for a clean description of the numerical scheme that mimics the essential features of its continuous counterpart. Furthermore, the stability analysis on a multi-block domain is simplified both for linear and nonlinear equations, since no problem-specific interface conditions must be derived and implemented. The theoretical developments are valid for all discretization methods that are included in the summation-by-parts framework. We exemplify the combined operator technique by considering a nonlinearly stable discrete formulation of the incompressible Navier-Stokes equations and perform calculations on an underlying multiblock domain.
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| 9. |
- Lundquist, Tomas, 1986-, et al.
(författare)
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A multi-domain summation-by-parts formulation for complex geometries
- 2022
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Ingår i: Journal of Computational Physics. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0021-9991 .- 1090-2716. ; 463
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Tidskriftsartikel (refereegranskat)abstract
- We combine existing summation-by-parts discretization methods to obtain a simplified numerical framework for partial differential equations posed on complex multi-block/element domains. The interfaces (conforming or non-conforming) between blocks are treated with inner-product-preserving interpolation operators, and the result is a high-order multi-block operator on summation-by-parts form that encapsulates both the metric terms as well as the interface treatments. This enables for a compact description of the numerical scheme that mimics the essential features of its continuous counterpart. Furthermore, the stability analysis on a multi-block domain is simplified for both for linear and nonlinear equations, since no problem-specific interface conditions need to be derived and implemented. We exemplify the combined operator technique by considering a nonlinearly stable discrete formulation of the incompressible Navier-Stokes equations and perform calculations on an underlying multi-block domain.
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| 10. |
- Lundquist, Tomas, 1986-, et al.
(författare)
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An analysis of non-conforming grid techniques for high order summation-by-parts metods
- 2017
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We derive a bound on the order of accuracy of interpolation operators for energy stable summation-by-parts discretizations on non-conforming multiblock meshes. The new theoretical result, which corroborate with experience from previous work, implies a local reduction in the formal accuracy of summation-by-parts discretizations based on diagonal norms. Numerical results confirm a corresponding reduction in convergence rate in both the maximum norm and the discrete L2 norm for a hyperbolic model problem.
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