
A New Stability Approach for PositivityPreserving Patankartype Schemes
Patankartype schemes are linearly implicit time integration methods des...
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Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing
We present Trixi.jl, a Julia package for adaptive highorder numerical s...
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Optimized RungeKutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics
We develop errorcontrol based time integration algorithms for compressi...
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On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations
We study the numerical error in solitary wave solutions of nonlinear dis...
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Preventing pressure oscillations does not fix local linear stability issues of entropybased splitform highorder schemes
Recently, it was discovered that the entropyconserving/dissipative high...
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A conservative fullydiscrete numerical method for the regularised shallow water wave equations
The paper proposes a new, conservative fullydiscrete scheme for the num...
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A purely hyperbolic discontinuous Galerkin approach for selfgravitating gas dynamics
One of the challenges when simulating astrophysical flows with selfgrav...
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Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts
We study nonlinear hyperbolic conservation laws with nonconvex flux and...
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A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
We develop general tools to construct fullydiscrete, conservative numer...
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PositivityPreserving Adaptive RungeKutta Methods
Many important differential equations model quantities whose value must ...
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FullyDiscrete Explicit Locally EntropyStable Schemes for the Compressible Euler and NavierStokes Equations
Recently, relaxation methods have been developed to guarantee the preser...
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A Class of A Stable Summation by Parts Time Integration Schemes
Since integration by parts is an important tool when deriving energy or ...
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Towards Green Computing: A Survey of Performance and Energy Efficiency of Different Platforms using OpenCL
When considering different hardware platforms, not just the timetosolu...
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General Relaxation Methods for InitialValue Problems with Application to Multistep Schemes
Recently, an approach known as relaxation has been developed for preserv...
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Relaxation RungeKutta Methods for Hamiltonian Problems
The recentlyintroduced relaxation approach for RungeKutta methods can ...
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On the robustness and performance of entropy stable discontinuous collocation methods for the compressible NavierStokes equations
In computational fluid dynamics, the demand for increasingly multidiscip...
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On the robustness and performance of entropy stable discontinuous collocation methods for the compressible NavieStokes equations
In computational fluid dynamics, the demand for increasingly multidiscip...
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Energy Stability of Explicit RungeKutta Methods for Nonautonomous or Nonlinear Problems
Many important initial value problems have the property that energy is n...
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Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators
In this article, discrete variants of several results from vector calcul...
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Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes
For the general class of residual distribution (RD) schemes, including m...
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Hendrik Ranocha
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