432 citations · 594 across the 35 of their papers we have counts for
36 papers
Towards provable energy-stable overset grid methods using sub-cell summation-by-parts operators
Jan Glaubitz, Joshua Lampert, Andrew R. Winters +1
Overset grid methods handle complex geometries by overlapping simpler, geometry-fitted grids to cover the original, more complex domain. However, ensuring their stability---particu…
Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators
Wasilij Barsukow, Christian Klingenberg, Lisa Lechner +3
The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values as independent degrees of freedom, based on ideas from fini…
Global Bounds for the Error in Solutions of Linear Hyperbolic Systems due to Inaccurate Boundary Geometry
David A. Kopriva, Andrew R. Winters, Jan Nordström
Meshes approximate the boundaries of a geometry when the boundaries are curved. The accuracy of the mesh then affects the error of computations of initial boundary value problems f…
An Energy Stable Nonlinear Incompressible Multi-Phase Flow Formulation
Jan Nordström, Arnaud. G. Malan
We show that a reformulation of the governing equations for incompressible multi-phase flow in the volume of fluid setting leads to a well defined energy rate. Weak nonlinear inflo…
An optimization-based construction procedure for function space based summation-by-parts operators on arbitrary grids
Jan Glaubitz, Jan Nordström, Philipp Öffner
We introduce a novel construction procedure for one-dimensional summation-by-parts (SBP) operators. Existing construction procedures for FSBP operators of the form p…
Energy Bounds for Discontinuous Galerkin Spectral Element Approximations of Well-Posed Overset Grid Problems for Hyperbolic Systems
David A. Kopriva, Andrew R. Winters, Jan Nordström
We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an app…
Exact symmetry conservation and automatic mesh refinement in discrete initial boundary value problems
Alexander Rothkopf, W. A. Horowitz, Jan Nordström
We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees…
A Skew-Symmetric Energy Stable Almost Dissipation Free Formulation of the Compressible Navier-Stokes Equations
Jan Nordström
We show that a specific skew-symmetric formulation of the nonlinear terms in the compressible Navier-Stokes equations leads to an energy rate in terms of surface integrals only. No…
The crucial role of Lagrange multipliers in a space-time symmetry preserving discretization scheme for IVPs
Alexander Rothkopf, Jan Nordström
In a recently developed variational discretization scheme for second order initial value problems ( J. Comput. Phys. 498, 112652 (2024) ), it was shown that the Noether charge asso…
An SBP-SAT Continuous Galerkin Finite Element Formulation for Smooth and Discontinuous Fields
Arnaud G. Malan, Jan Nordstrom
The high-order accurate continuous Galerkin finite element method offers attractive computational efficiency for computational fluid dynamics. A challenge is however spurious oscil…
A superconvergent stencil-adaptive SBP-SAT finite difference scheme
Viktor Linders, Mark Carpenter, Jan Nordström
A stencil-adaptive SBP-SAT finite difference scheme is shown to display superconvergent behavior. Applied to the linear advection equation, it has a convergence rate $\mathcal{O}(Δ…
A symmetry and Noether charge preserving discretization of initial value problems
Alexander Rothkopf, Jan Nordström
Taking insight from the theory of general relativity, where space and time are treated on the same footing, we develop a novel geometric variational discretization for second order…
Uncertain Data in Initial Boundary Value Problems: Impact on Short and Long Time Predictions
Jan Nordström
We investigate the influence of uncertain data on solutions to initial boundary value problems. Uncertainty in the forcing function, initial conditions and boundary conditions are…
A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations
Mojalefa P. Nchupang, Arnaud G. Malan, Fredrik Laurén +1
In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimate…
Summation-by-parts operators for general function spaces: The second derivative
Jan Glaubitz, Simon-Christian Klein, Jan Nordström +1
Many applications rely on solving time-dependent partial differential equations (PDEs) that include second derivatives. Summation-by-parts (SBP) operators are crucial for developin…
Nonlinear Boundary Conditions for Initial Boundary Value Problems with Applications in Computational Fluid Dynamics
Jan Nordström
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. Th…
Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes
Tomas Lundquist, Andrew Winters, Jan Nordström
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development,…
A method-of-lines framework for energy stable arbitrary Lagrangian-Eulerian methods
Tomas Lundquist, Arnaud Malan, Jan Nordström
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 developmen…
Nonlinear Boundary Conditions for Energy and Entropy Stable Initial Boundary Value Problems in Computational Fluid Dynamics
Jan Nordström
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step proc…
Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction
Jan Glaubitz, Simon-Christian Klein, Jan Nordström +1
Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recen…
A new variational discretization technique for initial value problems bypassing governing equations
Alexander Rothkopf, Jan Nordström
Motivated by the fact that both the classical and quantum description of nature rest on causality and a variational principle, we develop a novel and highly versatile discretizatio…
Energy-stable global radial basis function methods on summation-by-parts form
Jan Glaubitz, Jan Nordström, Philipp Öffner
Radial basis function methods are powerful tools in numerical analysis and have demonstrated good properties in many different simulations. However, for time-dependent partial diff…
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems II: Entropy Bounded Formulations for Nonlinear Conservation Laws
David A. Kopriva, Gregor J. Gassner, Jan Nordstrom
We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximat…
Summation-by-parts operators for general function spaces
Jan Glaubitz, Jan Nordström, Philipp Öffner
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equati…