
arXiv: 1703.00325
handle: 11383/2068175 , 11573/1280527 , 2318/1647270
This work is dedicated to the development and comparison of WENO-type reconstructions for hyperbolic systems of balance laws. We are particularly interested in high order shock capturing non-oscillatory schemes with uniform accuracy within each cell and low spurious effects. We need therefore to develop a tool to measure the artifacts introduced by a numerical scheme. To this end, we study the deformation of a single Fourier mode and introduce the notion of distorsive errors, which measure the amplitude of the spurious modes created by a discrete derivative operator. Further we refine this notion with the idea of temperature, in which the amplitude of the spurious modes is weighted with its distance in frequency space from the exact mode. Following this approach linear schemes have zero temperature, but to prevent oscillations it is necessary to introduce nonlinearities in the scheme, thus increasing their temperature. However it is important to heat the linear scheme just enough to prevent spurious oscillations. With several tests we show that the newly introduced CWENOZ schemes are cooler than other existing WENO-type operators, while maintaining good non-oscillatory properties.
Artificial diffusion and dispersion, Distorsive effects, Essentially non-oscillatory schemes, Finite volumes, Numerical Analysis, Finite volume methods applied to problems in fluid mechanics, Numerical Analysis (math.NA), essentially non-oscillatory schemes; finite volumes; artificial diffusion and dispersion; distorsive effects., Artificial diffusion and dispersion; distorsive effects; essentially non-oscillatory schemes; finite volumes, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Hyperbolic conservation laws, FOS: Mathematics, artificial diffusion and dispersion, distorsive effects, essentially non-oscillatory schemes, finite volumes
Artificial diffusion and dispersion, Distorsive effects, Essentially non-oscillatory schemes, Finite volumes, Numerical Analysis, Finite volume methods applied to problems in fluid mechanics, Numerical Analysis (math.NA), essentially non-oscillatory schemes; finite volumes; artificial diffusion and dispersion; distorsive effects., Artificial diffusion and dispersion; distorsive effects; essentially non-oscillatory schemes; finite volumes, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Hyperbolic conservation laws, FOS: Mathematics, artificial diffusion and dispersion, distorsive effects, essentially non-oscillatory schemes, finite volumes
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 42 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
