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Publications (10 of 214) Show all publications
Wahlsten, M. & Nordström, J. (2018). An efficient hybrid method for uncertainty quantification. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>An efficient hybrid method for uncertainty quantification
2018 (English)Report (Other academic)
Abstract [en]

A technique for coupling an intrusive and non-intrusive uncertainty quantification method is proposed. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. A strongly stable coupling procedure between the two methods at an interface is constructed. The efficiency of the hybrid method is exemplified using a hyperbolic system of equations, and verified by numerical experiments.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 20
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:3
Keyword
Uncertainty quantification, numerical integration, stochastic Galerkin, polynomial chaos, coupling, projection operator
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-146036 (URN)LiTH-MAT-R--2018/03--SE (ISRN)
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2018-04-09Bibliographically approved
Nordström, J. & Ghasemi, F. (2018). Corrigendum to “On the relation between conservation and dual consistency for summation-by-parts schemes”[J. Comput. Phys. 344 (2017) 437–439]. Journal of Computational Physics, 360, 247-247
Open this publication in new window or tab >>Corrigendum to “On the relation between conservation and dual consistency for summation-by-parts schemes”[J. Comput. Phys. 344 (2017) 437–439]
2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 360, p. 247-247Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Academic Press, 2018
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-145718 (URN)10.1016/j.jcp.2018.02.046 (DOI)
Available from: 2018-03-19 Created: 2018-03-19 Last updated: 2018-03-27Bibliographically approved
Eriksson, S. & Nordström, J. (2018). Finite difference schemes with transferable interfaces for parabolic problems. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Finite difference schemes with transferable interfaces for parabolic problems
2018 (English)Report (Other academic)
Abstract [en]

We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 16
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:1
Keyword
Finite difference methods, summation-by-parts, high order accuracy, dual consistency, superconvergence, interfaces
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-146078 (URN)LiTH-MAT-R--2018/01--SE (ISRN)
Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2018-04-06Bibliographically approved
Wahlsten, M. & Nordström, J. (2018). Stochastic Galerkin Projection and Numerical Integration for Stochastic Investigations of the Viscous Burgers’ Equation. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Stochastic Galerkin Projection and Numerical Integration for Stochastic Investigations of the Viscous Burgers’ Equation
2018 (English)Report (Other academic)
Abstract [en]

We consider a stochastic analysis of the non-linear viscous Burgers’ equation and focus on the comparison between intrusive and non-intrusive uncer- tainty quantification methods. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. The two methods are applied to a provably stable formulation of the viscous Burgers’ equation, and compared. As measures of comparison: variance size, computational efficiency and accuracy are used.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 14
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:2
Keyword
Uncertainty quantification, stochastic data, polynomial chaos, stochastic Galerkin, intrusive methods, non-intrusive methods, Burgers’ equation
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-146038 (URN)LiTH-MAT-R--2018/02--SE (ISRN)
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2018-04-09Bibliographically approved
Nordström, J. & Linders, V. (2018). Well-posed and stable transmission problems. Journal of Computational Physics, 364, 95-110
Open this publication in new window or tab >>Well-posed and stable transmission problems
2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 364, p. 95-110Article in journal (Refereed) Published
Abstract [en]

We introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability are analysed for continuous and discrete problems using both strong and weak formulations, and a general transmission condition is obtained. The theory is applied to the coupling of fluid-acoustic models, multi-grid implementations, adaptive mesh refinements, multi-block formulations and numerical filtering.

Place, publisher, year, edition, pages
Elsevier, 2018
Keyword
Transmission problems; Well-posedness; Stability; Adaptive mesh refinement; Numerical filter; Multi-grid
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-146206 (URN)10.1016/j.jcp.2018.03.003 (DOI)
Available from: 2018-03-29 Created: 2018-03-29 Last updated: 2018-03-29
Ruggiu, A. A., Weinerfelt, P. & Nordström, J. (2017). A new multigrid formulation for high order finite difference methods on summation-by-parts form. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>A new multigrid formulation for high order finite difference methods on summation-by-parts form
2017 (English)Report (Other academic)
Abstract [en]

Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 32
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2017:08
Keyword
High order finite difference methods, summation-by-parts, multigrid, restriction and prolongation operators, convergence acceleration
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-138955 (URN)LiTH-MAT-R--2017/08--SE (ISRN)
Available from: 2017-06-27 Created: 2017-06-27 Last updated: 2018-01-19Bibliographically approved
Delorme, Y. T., Puri, K., Nordström, J., Linders, V., Dong, S. & Frankel, S. H. (2017). A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains. Computers & Fluids, 150, 84-94
Open this publication in new window or tab >>A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains
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2017 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 150, p. 84-94Article in journal (Refereed) Published
Abstract [en]

Incompressible Navier-Stokes solvers based on the projection method often require an expensive numerical solution of a Poisson equation for a pressure-like variable. This often involves linear system solvers based on iterative and multigrid methods which may limit the ability to scale to large numbers of processors. The artificial compressibility method (ACM) [6] introduces a time derivative of the pressure into the incompressible form of the continuity equation creating a coupled closed hyperbolic system that does not require a Poisson equation solution and allows for explicit time-marching and localized stencil numerical methods. Such a scheme should theoretically scale well on large numbers of CPUs, GPU'€™s, or hybrid CPU-GPU architectures. The original ACM was only valid for steady flows and dual-time stepping was often used for time-accurate simulations. Recently, Clausen [7] has proposed the entropically damped artificial compressibility (EDAC) method which is applicable to both steady and unsteady flows without the need for dual-time stepping. The EDAC scheme was successfully tested with both a finite-difference MacCormack'€™s method for the two-dimensional lid driven cavity and periodic double shear layer problem and a finite-element method for flow over a square cylinder, with scaling studies on the latter to large numbers of processors. In this study, we discretize the EDAC formulation with a new optimized high-order centered finite-difference scheme and an explicit fourth-order Runge-€“Kutta method. This is combined with an immersed boundary method to efficiently treat complex geometries and a new robust outflow boundary condition to enable higher Reynolds number simulations on truncated domains. Validation studies for the Taylor-€“Green Vortex problem and the lid driven cavity problem in both 2D and 3D are presented. An eddy viscosity subgrid-scale model is used to enable large eddy simulations for the 3D cases. Finally, an application to flow over a sphere is presented to highlight the boundary condition and performance comparisons to a traditional incompressible Navier-€“Stokes solver is shown for the 3D lid driven cavity. Overall, the combined EDAC formulation and discretization is shown to be both effective and affordable.

Place, publisher, year, edition, pages
Elsevier, 2017
Keyword
Artificial compressibility method, EDAC, High-order numerical methods, Large Eddy simulation
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-136507 (URN)10.1016/j.compfluid.2017.03.030 (DOI)000401219000007 ()
Note

Funding agencies: Rosenblatt Chair within the faculty of Mechanical Engineering; Zeff Fellowship Trust

Available from: 2017-04-19 Created: 2017-04-19 Last updated: 2017-11-20Bibliographically approved
Ghasemi, F. & Nordström, J. (2017). Coupling Requirements for Multiphysics Problems Posed on Two Domains. SIAM Journal on Numerical Analysis, 55(6), 2885-2904
Open this publication in new window or tab >>Coupling Requirements for Multiphysics Problems Posed on Two Domains
2017 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 55, no 6, p. 2885-2904Article in journal (Refereed) Published
Abstract [en]

We consider two hyperbolic systems in first order form of different size posed on two domains. Our ambition is to derive general conditions for when the two systems can and cannot be coupled. The adjoint equations are derived and well-posedness of the primal and dual problems is discussed. By applying the energy method, interface conditions for the primal and dual problems are derived such that the continuous problems are well posed. The equations are discretized using a high order finite difference method in summation-by-parts form and the interface conditions are imposed weakly in a stable way, using penalty formulations. It is shown that one specic choice of penalty matrices leads to a dual consistent scheme. By considering an example, it is shown that the correct physical coupling conditions are contained in the set of well posed coupling conditions. It is also shown that dual consistency leads to superconverging functionals and reduced stiffness.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2017
Keyword
well posed problems, high order finite diffrences, stability, summation-by-parts, weak interface conditions, dual consistency, stiffness, superconvergence
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-143261 (URN)10.1137/16M1087710 (DOI)000418663500015 ()
Available from: 2017-11-28 Created: 2017-11-28 Last updated: 2018-01-26Bibliographically approved
O'Reilly, O., Lundquist, T., Dunham, E. M. & Nordström, J. (2017). Energy stable and high-order-accurate finite difference methods on staggered grids. Journal of Computational Physics, 346, 572-589
Open this publication in new window or tab >>Energy stable and high-order-accurate finite difference methods on staggered grids
2017 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 346, p. 18p. 572-589Article in journal (Refereed) Published
Abstract [en]

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

Place, publisher, year, edition, pages
Academic Press, 2017. p. 18
Keyword
Staggered grids High order finite difference methods Summation-by-parts Weakly enforced boundary conditions Energy stability Wave propagation
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-139343 (URN)10.1016/j.jcp.2017.06.030 (DOI)000406465000029 ()2-s2.0-85021952350 (Scopus ID)
Note

Funding agencies: Department of Geophysics at Stanford University

Available from: 2017-07-11 Created: 2017-07-11 Last updated: 2018-03-27Bibliographically approved
Nordström, J. & La Cognata, C. (2017). Energy Stable Boundary Conditions for the Nonlinear Incompressible Navier-Stokes Equations. Linköping University Electronic Press
Open this publication in new window or tab >>Energy Stable Boundary Conditions for the Nonlinear Incompressible Navier-Stokes Equations
2017 (English)Report (Other academic)
Abstract [en]

The nonlinear incompressible Navier-Stokes equations with boundary conditions at far fields and solid walls is considered. Two different formulations of boundary conditions are derived using the energy method. Both formulations are implemented in both strong and weak form and lead to an estimate of the velocity field. Equipped with energy bounding boundary conditions, the problem is approximated by using difference operators on summation-by-parts form and weak boundary and initial conditions. By mimicking the continuous analysis, the resulting semi-discrete as well as fully discrete scheme are shown to be provably stable, divergence free and high-order accurate.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2017. p. 31
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2017:9
Keyword
Navier-Stokes equations, incompressible, boundary conditions, energy estimate, stability, summation-by-parts, high-order accuracy, divergence free
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-139730 (URN)LiTH-MAT-R--2017/09--SE (ISRN)
Available from: 2017-08-14 Created: 2017-08-14 Last updated: 2017-09-05Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-7972-6183

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