Nordström, Jan 1953
Overview
Works:  149 works in 205 publications in 3 languages and 786 library holdings 

Roles:  Author, Arranger, Other, Contributor, the, Thesis advisor 
Publication Timeline
.
Most widely held works by
Jan Nordström
Polynomial chaos methods for hyperbolic partial differential equations : numerical techniques for fluid dynamics problems
in the presence of uncertainties by
Mass Per Pettersson(
)
11 editions published in 2015 in English and held by 281 WorldCat member libraries worldwide
This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical samplingbased techniques. The approach described in the text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and nonlinear convectiondiffusion equations and for a systems of conservation laws; a detailed wellposedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable highorder finitedifference methods based on summationbyparts operators for smooth problems, and robust shockcapturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but not necessary
11 editions published in 2015 in English and held by 281 WorldCat member libraries worldwide
This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical samplingbased techniques. The approach described in the text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and nonlinear convectiondiffusion equations and for a systems of conservation laws; a detailed wellposedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable highorder finitedifference methods based on summationbyparts operators for smooth problems, and robust shockcapturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but not necessary
High order finite difference methods, multidimensional linear problems and curvilinear coordinates by
Jan Nordström(
Book
)
5 editions published in 1999 in English and held by 96 WorldCat member libraries worldwide
Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met
5 editions published in 1999 in English and held by 96 WorldCat member libraries worldwide
Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met
Boundary and interface conditions for high order finite difference methods applied to the Euler and NavierStokes equations by
Jan Nordström(
Book
)
6 editions published in 1998 in English and held by 95 WorldCat member libraries worldwide
Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and NavierStokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems
6 editions published in 1998 in English and held by 95 WorldCat member libraries worldwide
Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and NavierStokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems
A stable and conservative interface treatment of arbitrary spatial accuracy by
Mark H Carpenter(
Book
)
3 editions published in 1998 in English and held by 91 WorldCat member libraries worldwide
3 editions published in 1998 in English and held by 91 WorldCat member libraries worldwide
Artificial boundary conditions for the NavierStokes equations by
Jan Nordström(
Book
)
5 editions published in 1993 in English and held by 13 WorldCat member libraries worldwide
5 editions published in 1993 in English and held by 13 WorldCat member libraries worldwide
Open boundary conditions for the NavierStokes Equation by
Jan Nordström(
Book
)
3 editions published in 1988 in English and held by 11 WorldCat member libraries worldwide
3 editions published in 1988 in English and held by 11 WorldCat member libraries worldwide
Sange for børn og andre mennesker, 3 dig og mig og alle os by
Bjarne Jes Hansen(
Recording
)
5 editions published in 1978 in Undetermined and Danish and held by 9 WorldCat member libraries worldwide
5 editions published in 1978 in Undetermined and Danish and held by 9 WorldCat member libraries worldwide
Wellposedness, stability and conservation for a discontinuous interface problem by
Cristina La Cognata(
)
2 editions published between 2014 and 2015 in English and held by 3 WorldCat member libraries worldwide
The advection equation is studied in a completely general two domain setting with different wavespeeds and a timeindependent jumpcondition at the interface separating the domains. Wellposedness and conservation criteria are derived for the initialboundaryvalue problem. The equations are semidiscretized using afinite dfference method on summationbyparts (SBP) form. The stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the simultaneous approximation term (SAT) procedure. Numerical simulations corroborate the theoretical finndings
2 editions published between 2014 and 2015 in English and held by 3 WorldCat member libraries worldwide
The advection equation is studied in a completely general two domain setting with different wavespeeds and a timeindependent jumpcondition at the interface separating the domains. Wellposedness and conservation criteria are derived for the initialboundaryvalue problem. The equations are semidiscretized using afinite dfference method on summationbyparts (SBP) form. The stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the simultaneous approximation term (SAT) procedure. Numerical simulations corroborate the theoretical finndings
Efficient fully discrete summationbyparts schemes for unsteady flow problems by Tomas Lundquist(
)
2 editions published between 2014 and 2015 in English and held by 3 WorldCat member libraries worldwide
We make an initial investigation into the numerical efficiency of a fully dis crete summationbyparts approach for unsteady flows. As a model problem for the NavierStokes equations we consider a twodimensional advection diffusion problem with a boundary layer. The problem is discretized in space using finite difference approximations on summationbyparts form together with weak boundary conditions, leading to optimal stability estimates. For the time integration part we consider various forms of high order summation byparts operators, and compare the results to other popular high order methods. To solve the resulting fully discrete equation system, we employ a multigrid scheme with dual time stepping
2 editions published between 2014 and 2015 in English and held by 3 WorldCat member libraries worldwide
We make an initial investigation into the numerical efficiency of a fully dis crete summationbyparts approach for unsteady flows. As a model problem for the NavierStokes equations we consider a twodimensional advection diffusion problem with a boundary layer. The problem is discretized in space using finite difference approximations on summationbyparts form together with weak boundary conditions, leading to optimal stability estimates. For the time integration part we consider various forms of high order summation byparts operators, and compare the results to other popular high order methods. To solve the resulting fully discrete equation system, we employ a multigrid scheme with dual time stepping
On Long Time Error Bounds for the Wave Equation on Second Order Form by
Jan Nordström(
)
2 editions published in 2018 in English and held by 3 WorldCat member libraries worldwide
Temporal error bounds for the wave equation expressed on second order form are investigated. We show that, with appropriate choices of boundary conditions, the time and space derivatives of the error are bounded even for long times. No long time bound on the error itself is obtained, although numerical experiments indicate that a bound exists
2 editions published in 2018 in English and held by 3 WorldCat member libraries worldwide
Temporal error bounds for the wave equation expressed on second order form are investigated. We show that, with appropriate choices of boundary conditions, the time and space derivatives of the error are bounded even for long times. No long time bound on the error itself is obtained, although numerical experiments indicate that a bound exists
The effect of uncertain geometries on advectiondiffusion of scalar quantities by
Markus Wahlsten(
)
2 editions published in 2017 in English and held by 3 WorldCat member libraries worldwide
The two dimensional advectiondiffusion equation in a stochastically varyinggeometry is considered. The varying domain is transformed into a fixed one andthe numerical solution is computed using a highorder finite difference formulationon summationbyparts form with weakly imposed boundary conditions. Statistics ofthe solution are computed nonintrusively using quadrature rules given by the probabilitydensity function of the random variable. As a quality control, we prove that thecontinuous problem is strongly wellposed, that the semidiscrete problem is stronglystable and verify the accuracy of the scheme. The technique is applied to a heat transferproblem in incompressible flow. Statistical properties such as confidence intervals andvariance of the solution in terms of two functionals are computed and discussed. Weshow that there is a decreasing sensitivity to geometric uncertainty as we graduallylower the frequency and amplitude of the randomness. The results are less sensitiveto variations in the correlation length of the geometry
2 editions published in 2017 in English and held by 3 WorldCat member libraries worldwide
The two dimensional advectiondiffusion equation in a stochastically varyinggeometry is considered. The varying domain is transformed into a fixed one andthe numerical solution is computed using a highorder finite difference formulationon summationbyparts form with weakly imposed boundary conditions. Statistics ofthe solution are computed nonintrusively using quadrature rules given by the probabilitydensity function of the random variable. As a quality control, we prove that thecontinuous problem is strongly wellposed, that the semidiscrete problem is stronglystable and verify the accuracy of the scheme. The technique is applied to a heat transferproblem in incompressible flow. Statistical properties such as confidence intervals andvariance of the solution in terms of two functionals are computed and discussed. Weshow that there is a decreasing sensitivity to geometric uncertainty as we graduallylower the frequency and amplitude of the randomness. The results are less sensitiveto variations in the correlation length of the geometry
High Order Finite Difference Approximations of Electromagnetic Wave Propagation Close to Material Discontinuities by
Jan Nordström(
)
2 editions published in 2003 in English and held by 3 WorldCat member libraries worldwide
Electromagnetic wave propagation close to a material discontinuity is simulated by using summation by part operators of second, fourth and sixth order accuracy. The interface conditions at the discontinuity are imposed by the simultaneous approximation term procedure. Stability is shown and the order of accuracy is verified numerically
2 editions published in 2003 in English and held by 3 WorldCat member libraries worldwide
Electromagnetic wave propagation close to a material discontinuity is simulated by using summation by part operators of second, fourth and sixth order accuracy. The interface conditions at the discontinuity are imposed by the simultaneous approximation term procedure. Stability is shown and the order of accuracy is verified numerically
Artificial boundary conditions for the NavierStokes equations by
Jan Nordström(
Book
)
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
Weak and strong wall boundary procedures and convergence to steadystate of the NavierStokes equations by
Jan Nordström(
)
3 editions published between 2011 and 2012 in English and held by 3 WorldCat member libraries worldwide
We study the influence of different implementations of noslip solid wall boundary conditions on the convergence to steadystate of the NavierStokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steadystate for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis
3 editions published between 2011 and 2012 in English and held by 3 WorldCat member libraries worldwide
We study the influence of different implementations of noslip solid wall boundary conditions on the convergence to steadystate of the NavierStokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steadystate for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis
Choral Music (Swedish)  AGNESTIG, C.B.(
)
in English and held by 3 WorldCat member libraries worldwide
in English and held by 3 WorldCat member libraries worldwide
Norrköpings arbetarrörelses historia : en populärvetenskaplig framställning by
Börje Hjorth(
Book
)
2 editions published in 1989 in Swedish and held by 3 WorldCat member libraries worldwide
2 editions published in 1989 in Swedish and held by 3 WorldCat member libraries worldwide
Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps by
David A Kopriva(
)
2 editions published between 2020 and 2021 in English and held by 3 WorldCat member libraries worldwide
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 RankineHugoniot(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 RankineHugoniot jump
2 editions published between 2020 and 2021 in English and held by 3 WorldCat member libraries worldwide
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 RankineHugoniot(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 RankineHugoniot jump
Elimination of first order errors in shock calculations by
Gunilla Kreiss(
Book
)
3 editions published between 1998 and 2001 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 1998 and 2001 in English and held by 3 WorldCat member libraries worldwide
Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems by
David A Kopriva(
)
2 editions published in 2017 in English and held by 3 WorldCat member libraries worldwide
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
2 editions published in 2017 in English and held by 3 WorldCat member libraries worldwide
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
On the Order of Accuracy for Difference Approximations of InitialBoundary Value Problems by
Magnus Svärd(
Book
)
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Iaccarino, Gianluca Thesis advisor
 Pettersson, Mass Per Author
 Carpenter, Mark H. (Mark Huitt) Author
 Institute for Computer Applications in Science and Engineering
 Gottlieb, David
 Linköpings universitet Matematiska institutionen Publisher
 Linköpings universitet Tekniska högskolan Publisher
 SpringerLink (Online service) Other
 Svärd, Magnus Author
 Flygtekniska försöksanstalten (Sweden) Other
Associated Subjects
Boundary value problems Differential equations Differential equations, HyperbolicNumerical solutions Differential equations, PartialNumerical solutions Diffusion Engineering Finite differences Fluid mechanics Fluids Galerkin methods Hydraulic engineering NavierStokes equations NavierStokes equationsNumerical solutions Numerical analysis