The Effect of the Differencing Scheme on the Numerical Diffusion in the Simulation of Macrosegregation

2006 ◽  
pp. 199-204
Author(s):  
B.C.H. Venneker ◽  
L. Katgerman
Keyword(s):  
Numerical Diffusion

scholarly journals Numerical Study on an Interface Compression Method for the Volume of Fluid Approach

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 80
Author(s):  
Yuria Okagaki ◽  
Taisuke Yonomoto ◽  
Masahiro Ishigaki ◽  
Yoshiyasu Hirose
Keyword(s):  
Linear Theory ◽  
Volume Fraction ◽  
Numerical Study ◽  
Volume Of Fluid ◽  
Interfacial Wave ◽  
Validation Process ◽  
Two Phase ◽  
Numerical Diffusion ◽  
Mesh Resolution ◽  
Water Reactors

Many thermohydraulic issues about the safety of light water reactors are related to complicated two-phase flow phenomena. In these phenomena, computational fluid dynamics (CFD) analysis using the volume of fluid (VOF) method causes numerical diffusion generated by the first-order upwind scheme used in the convection term of the volume fraction equation. Thus, in this study, we focused on an interface compression (IC) method for such a VOF approach; this technique prevents numerical diffusion issues and maintains boundedness and conservation with negative diffusion. First, on a sufficiently high mesh resolution and without the IC method, the validation process was considered by comparing the amplitude growth of the interfacial wave between a two-dimensional gas sheet and a quiescent liquid using the linear theory. The disturbance growth rates were consistent with the linear theory, and the validation process was considered appropriate. Then, this validation process confirmed the effects of the IC method on numerical diffusion, and we derived the optimum value of the IC coefficient, which is the parameter that controls the numerical diffusion.

scholarly journals EDGE: a new approach to suppressing numerical diffusion in adaptive mesh simulations of galaxy formation

2020 ◽  
Vol 501 (2) ◽  
pp. 1755-1765
Author(s):  
Andrew Pontzen ◽  
Martin P Rey ◽  
Corentin Cadiou ◽  
Oscar Agertz ◽  
Romain Teyssier ◽  
...  
Keyword(s):  
Star Formation ◽  
Galaxy Formation ◽  
Adaptive Mesh Refinement ◽  
Large Scale ◽  
Initial Conditions ◽  
Dwarf Galaxy ◽  
High Redshift ◽  
Morphological Structure ◽  
Adaptive Mesh ◽  
Numerical Diffusion

ABSTRACT We introduce a new method to mitigate numerical diffusion in adaptive mesh refinement (AMR) simulations of cosmological galaxy formation, and study its impact on a simulated dwarf galaxy as part of the ‘EDGE’ project. The target galaxy has a maximum circular velocity of $21\, \mathrm{km}\, \mathrm{s}^{-1}$ but evolves in a region that is moving at up to $90\, \mathrm{km}\, \mathrm{s}^{-1}$ relative to the hydrodynamic grid. In the absence of any mitigation, diffusion softens the filaments feeding our galaxy. As a result, gas is unphysically held in the circumgalactic medium around the galaxy for $320\, \mathrm{Myr}$, delaying the onset of star formation until cooling and collapse eventually triggers an initial starburst at z = 9. Using genetic modification, we produce ‘velocity-zeroed’ initial conditions in which the grid-relative streaming is strongly suppressed; by design, the change does not significantly modify the large-scale structure or dark matter accretion history. The resulting simulation recovers a more physical, gradual onset of star formation starting at z = 17. While the final stellar masses are nearly consistent ($4.8 \times 10^6\, \mathrm{M}_{\odot }$ and $4.4\times 10^6\, \mathrm{M}_{\odot }$ for unmodified and velocity-zeroed, respectively), the dynamical and morphological structure of the z = 0 dwarf galaxies are markedly different due to the contrasting histories. Our approach to diffusion suppression is suitable for any AMR zoom cosmological galaxy formation simulations, and is especially recommended for those of small galaxies at high redshift.

scholarly journals The study of the numerical diffusion in computational calculation

2020 ◽  
Vol 310 ◽  
pp. 00039
Author(s):  
Kamila Kotrasova ◽  
Vladimira Michalcova
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Numerical Simulation ◽  
Continuity Equation ◽  
Cfd Simulation ◽  
Flow Process ◽  
Ansys Fluent ◽  
Numerical Diffusion ◽  
Mesh Density ◽  
Computational Calculation

The numerical simulation of flow process and heat transfer phenomena demands the solution of continuous differential equation and energy-conservation equations coupled with the continuity equation. The choosing of computation parameters in numerical simulation of computation domain have influence on accuracy of obtained results. The choose parameters, as mesh density, mesh type and computation procedures, for the numerical diffusion of computation domain were analysed and compared. The CFD simulation in ANSYS – Fluent was used for numerical simulation of 3D stational temperature flow of the computation domain.

scholarly journals Numerical and Physical Diffusion: Can Wave Prediction Models Resolve Directional Spread?

2005 ◽  
Vol 22 (7) ◽  
pp. 886-895 ◽  
Author(s):  
F. Ardhuin ◽  
T. H. C. Herbers
Keyword(s):  
Continental Shelf ◽  
Prediction Models ◽  
Spectral Band ◽  
Wave Spectrum ◽  
Single Frequency ◽  
Propagation Time ◽  
Time Step ◽  
Numerical Diffusion ◽  
Wave Prediction ◽  
Lagrangian Scheme

Abstract A new semi-Lagrangian advection scheme called multistep ray advection is proposed for solving the spectral energy balance equation of ocean surface gravity waves. Existing so-called piecewise ray methods advect wave energy over a single time step using “pieces” of ray trajectories, after which the spectrum is updated with source terms representing various physical processes. The generalized scheme presented here allows for an arbitrary number N of advection time steps along the same rays, thus reducing numerical diffusion, and still including source-term variations every time step. Tests are performed for alongshore uniform bottom topography, and the effects of two types of discretizations of the wave spectrum are investigated, a finite-bandwidth representation and a single frequency and direction per spectral band. In the limit of large N, both the accuracy and computation cost of the method increase, approaching a nondiffusive fully Lagrangian scheme. Even for N = 1 the semi-Lagrangian scheme test results show less numerical diffusion than predictions of the commonly used first-order upwind finite-difference scheme. Application to the refraction and shoaling of narrow swell spectra across a continental shelf illustrates the importance of controlling numerical diffusion. Numerical errors in a single-step (Δt = 600 s) scheme implemented on the North Carolina continental shelf (typical swell propagation time across the shelf is about 3 h) are shown to be comparable to the angular diffusion predicted by the wave–bottom Bragg scattering theory, in particular for narrow directional spectra, suggesting that the true directional spread of swell may not always be resolved in existing wave prediction models, because of excessive numerical diffusion. This diffusion is effectively suppressed in cases presented here with a four-step semi-Lagrangian scheme, using the same value of Δt.

scholarly journals Broadening of Modeled Cloud Droplet Spectra Using Bin Microphysics in an Eulerian Spatial Domain

2018 ◽  
Vol 75 (11) ◽  
pp. 4005-4030 ◽  
Author(s):  
Hugh Morrison ◽  
Mikael Witte ◽  
George H. Bryan ◽  
Jerry Y. Harrington ◽  
Zachary J. Lebo
Keyword(s):  
Cloud Condensation Nuclei ◽  
Cloud Droplet ◽  
Droplet Size Distribution ◽  
Dynamical Models ◽  
Mixing Processes ◽  
Numerical Diffusion ◽  
Vertical Advection ◽  
1D Model ◽  
Bin Microphysics ◽  
Condensational Growth

Abstract This study investigates droplet size distribution (DSD) characteristics from condensational growth and transport in Eulerian dynamical models with bin microphysics. A hierarchy of modeling frameworks is utilized, including parcel, one-dimensional (1D), and three-dimensional large-eddy simulation (LES). The bin DSDs from the 1D model, which includes only vertical advection and condensational growth, are nearly as broad as those from the LES and in line with observed DSD widths for stratocumulus clouds. These DSDs are much broader than those from Lagrangian microphysical calculations within a parcel framework that serve as a numerical benchmark for the 1D tests. In contrast, the bin-modeled DSDs are similar to the Lagrangian microphysical benchmark for a rising parcel in which Eulerian transport is not considered. These results indicate that numerical diffusion associated with vertical advection is a key contributor to broadening DSDs in the 1D model and LES. This DSD broadening from vertical numerical diffusion is unphysical, in contrast to the physical mixing processes that previous studies have indicated broaden DSDs in real clouds. It is proposed that artificial DSD broadening from vertical numerical diffusion compensates for underrepresented horizontal variability and mixing of different droplet populations in typical LES configurations with bin microphysics, or the neglect of other mechanisms that broaden DSDs such as growth of giant cloud condensation nuclei. These results call into question the ability of Eulerian dynamical models with bin microphysics to investigate the physical mechanisms for DSD broadening, even though they may reasonably simulate overall DSD characteristics.

Discussion of “Linear Reservoirs and Numerical Diffusion”

1981 ◽  
Vol 107 (2) ◽  
pp. 251-251
Author(s):  
Witold G. Strupczewski ◽  
Zbigniew W. Kundzewicz
Keyword(s):  
Numerical Diffusion

scholarly journals The Numerical Diffusion Effect on the CFD Simulation Accuracy of Velocity and Temperature Field for the Application of Sustainable Architecture Methodology

2020 ◽  
Vol 12 (23) ◽  
pp. 10173
Author(s):  
Vladimíra Michalcová ◽  
Kamila Kotrasová
Keyword(s):  
Temperature Field ◽  
Cfd Simulation ◽  
Flow Direction ◽  
Three Dimensional ◽  
Stationary Flow ◽  
Navier Stokes ◽  
Ansys Fluent ◽  
Simulation Accuracy ◽  
Numerical Diffusion ◽  
Diffusion Temperature

Numerical simulation of fluid flow and heat or mass transfer phenomenon requires numerical solution of Navier–Stokes and energy-conservation equations, together with the continuity equation. The basic problem of solving general transport equations by the Finite Volume Method (FVM) is the exact calculation of the transport quantity. Numerical or false diffusion is a phenomenon of inserting errors in calculations that threaten the accuracy of the computational solution. The paper compares the physical accuracy of the calculation in the Computational Fluid Dynamics (CFD) code in Ansys Fluent using the offered discretization calculation schemes, methods of solving the gradients of the transport quantity on the cell walls, and the influence of the mesh type. The paper offers possibilities on how to reduce numerical errors. In the calculation area, the sharp boundary of two areas with different temperatures is created in the flow direction. The three-dimensional (3D) stationary flow of the fictitious gas is simulated using FVM so that only advective transfer, in terms of momentum and heat, arises. The subject of the study is to determine the level of numerical diffusion (temperature field scattering) and to evaluate the values of the transport quantity (temperature), which are outside the range of specified boundary conditions at variously set calculation parameters.

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