| 41. |
- Kopriva, David A., et al.
(författare)
-
Error boundedness of discontinuous Galerkin spectral element approximations of hyperbolic problems
- 2016
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations. We show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lower value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved.
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| 42. |
- Kopriva, David A., et al.
(författare)
-
Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems
- 2017
-
Ingår i: Journal of Scientific Computing. - : Springer Science and Business Media LLC. - 0885-7474 .- 1573-7691. ; 72:1, s. 314-330
-
Tidskriftsartikel (refereegranskat)abstract
- We examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations. We show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lower value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved.
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| 43. |
- Kopriva, David A., et al.
(författare)
-
On the theoretical foundation of overset grid methods for hyperbolic problems : Well-posedness and conservation
- 2022
-
Ingår i: Journal of Computational Physics. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0021-9991 .- 1090-2716. ; 448
-
Tidskriftsartikel (refereegranskat)abstract
- We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space dimension, for both scalar equations and systems of equations, the problem where one domain partially oversets another is well-posed when characteristic coupling conditions are used. If a system cannot be diagonalized, as is usually the case in multiple space dimensions, then the energy method does not give proper bounds in terms of initial and boundary data. For those problems, we propose a novel penalty approach. We show, by using a global energy that accounts for the energy in the overlap region of the domains, that under well-defined conditions on the coupling matrices the penalized overset domain problems are energy bounded, conservative, well-posed and have solutions equivalent to the original single domain problem.
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| 44. |
- Kopriva, David A., et al.
(författare)
-
On the theoretical foundation of overset grid methods for hyperbolic problems II : Entropy bounded formulations for nonlinear conservation laws
- 2022
-
Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 471
-
Tidskriftsartikel (refereegranskat)abstract
- We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The entropy conserving formulation imposes a two-way coupling at the artificial interface boundaries through nonlinear penalty functions that vanish when the solutions coincide. The penalty functions are expressed in terms of entropy conserving fluxes originally introduced for finite volume schemes. In addition to the interface coupling, which is required, entropy dissipation and coupling can optionally be added through the use of linear penalties within the overlap region.
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| 45. |
- Kopriva, David A., et al.
(författare)
-
Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps
- 2021
-
Ingår i: Journal of Scientific Computing. - : Springer. - 0885-7474 .- 1573-7691. ; 88:1
-
Tidskriftsartikel (refereegranskat)abstract
- We use the behavior of the L2 norm of the solutions of linear hyperbolic equations withdiscontinuous coefficient matrices as a surrogate to infer stability of discontinuous Galerkinspectral element methods (DGSEM). Although the L2 norm is not bounded in terms of theinitial data for homogeneous and dissipative boundary conditions for such systems, the L2norm is easier to work with than a norm that discounts growth due to the discontinuities. Weshow that the DGSEM with an upwind numerical flux that satisfies the Rankine–Hugoniot(or conservation) condition has the same energy bound as the partial differential equationdoes in the L2 norm, plus an added dissipation that depends on how much the approximatesolution fails to satisfy the Rankine–Hugoniot jump.
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| 46. |
- Soriano, S, et al.
(författare)
-
Rapid regulation of K(ATP) channel activity by 17{beta}-estradiol in pancreatic {beta}-cells involves the estrogen receptor {beta} and the atrial natriuretic peptide receptor
- 2009
-
Ingår i: Molecular endocrinology (Baltimore, Md.). - : The Endocrine Society. - 1944-9917 .- 0888-8809. ; 23:12, s. 1973-1982
-
Tidskriftsartikel (refereegranskat)abstract
- The ATP-sensitive potassium (KATP) channel is a key molecule involved in glucose-stimulated insulin secretion. The activity of this channel regulates β-cell membrane potential, glucose- induced [Ca2+]i signals, and insulin release. In this study, the rapid effect of physiological concentrations of 17β-estradiol (E2) on KATP channel activity was studied in intact β-cells by use of the patch-clamp technique. When cells from wild-type (WT) mice were used, 1 nm E2 rapidly reduced KATP channel activity by 60%. The action of E2 on KATP channel was not modified in β-cells from ERα−/− mice, yet it was significantly reduced in cells from ERβ−/− mice. The effect of E2 was mimicked by the ERβ agonist 2,3-bis(4-hydroxyphenyl)-propionitrile (DPN). Activation of ERβ by DPN enhanced glucose-induced Ca2+ signals and insulin release. Previous evidence indicated that the acute inhibitory effects of E2 on KATP channel activity involve cyclic GMP and cyclic GMP-dependent protein kinase. In this study, we used β-cells from mice with genetic ablation of the membrane guanylate cyclase A receptor for atrial natriuretic peptide (also called the atrial natriuretic peptide receptor) (GC-A KO mice) to demonstrate the involvement of this membrane receptor in the rapid E2 actions triggered in β-cells. E2 rapidly inhibited KATP channel activity and enhanced insulin release in islets from WT mice but not in islets from GC-A KO mice. In addition, DPN reduced KATP channel activity in β-cells from WT mice, but not in β-cells from GC-A KO mice. This work unveils a new role for ERβ as an insulinotropic molecule that may have important physiological and pharmacological implications.
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| 47. |
- Storry, Jill R., et al.
(författare)
-
International Society of Blood Transfusion Working Party on Red Cell Immunogenetics and Blood Group Terminology : Report of the Dubai, Copenhagen and Toronto meetings
- 2019
-
Ingår i: Vox Sanguinis. - : Wiley. - 0042-9007. ; 114:1, s. 95-102
-
Tidskriftsartikel (refereegranskat)abstract
- Background and objectives: The International Society of Blood Transfusion (ISBT) Working Party for Red Cell Immunogenetics and Blood Group Terminology meets in association with the ISBT congress and has met three times since the last report: at the international meetings held in Dubai, United Arab Emirates, September 2016 and Toronto, Canada, June 2018; and at a regional congress in Copenhagen, Denmark, June 2017 for an interim session. Methods: As in previous meetings, matters pertaining to blood group antigen nomenclature and classification were discussed. New blood group antigens were approved and named according to the serologic and molecular evidence presented. Results and conclusions: Fifteen new blood group antigens were added to eight blood group systems. One antigen was made obsolete based on additional data. Consequently, the current total of blood group antigens recognized by the ISBT is 360, of which 322 are clustered within 36 blood groups systems. The remaining 38 antigens are currently unassigned to a known system. Clinically significant blood group antigens continue to be discovered, through serology/sequencing and/or recombinant or genomic technologies.
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| 48. |
- Wintermeyer, Niklas, et al.
(författare)
-
An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
- 2017
-
Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 340, s. 200-242
-
Tidskriftsartikel (refereegranskat)abstract
- We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non- constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretisation exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretisation of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.
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| 49. |
- Winters, Andrew Ross, et al.
(författare)
-
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations
- 2021. - 1
-
Ingår i: Efficient high-order discretizations for computational fluid dynamics. - Cham : Springer. - 9783030606107 ; , s. 117-196
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.
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| 50. |
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