Effects Of Numerical Dissipation Research Articles

The Effects of Numerical Dissipation on Hurricane Rapid Intensification With Observational Heating

AbstractThe computational fluid dynamics of hurricane rapid intensification (RI) is examined through idealized simulations using two codes: a community‐based, finite‐difference/split‐explicit model (WRF) and a spectral‐element/semi‐implicit model (NUMA). The focus of the analysis is on the effects of implicit numerical dissipation (IND) in the energetics of the vortex response to heating, which embodies the fundamental dynamics in the hurricane RI process. The heating considered here is derived from observations: four‐dimensional, fully nonlinear, latent heating/cooling rates calculated from airborne Doppler radar measurements collected in a hurricane undergoing RI. The results continue to show significant IND in WRF relative to NUMA with a reduction in various intensity metrics: (a) time‐integrated, mean kinetic energy values in WRF are ∼20% lower than NUMA and (b) peak, localized wind speeds in WRF are ∼12 m/s lower than NUMA. Values of the eddy diffusivity in WRF need to be reduced by ∼50% from those in NUMA to produce a similar intensity time series. Kinetic energy budgets demonstrate that the pressure contribution is the main factor in the model differences with WRF producing smaller energy input to the vortex by ∼23%, on average. The low‐order spatial discretization of the pressure gradient in WRF is implicated in the IND. In addition, the eddy transport term is found to have a largely positive impact on the vortex intensification with a mean contribution of ∼20%. Overall, these results have important implications for the research and operational forecasting communities that use WRF and WRF‐like numerical models.

Wave Propagation Studies in Numerical Wave Tanks with Weakly Compressible Smoothed Particle Hydrodynamics

Generation and propagation of waves in a numerical wave tank constructed using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) are considered here. Numerical wave tank simulations have been carried out with implementations of different Wendland kernels in conjunction with different numerical dissipation schemes. The simulations were accelerated by using General Process Graphics Processing Unit (GPGPU) computing to utilize the massively parallel nature of the simulations and thus improve process efficiency. Numerical experiments with short domains have been carried out to validate the dissipation schemes used. The wave tank experiments consist of piston-type wavemakers and appropriate passive absorption arrangements to facilitate comparisons with theoretical predictions. The comparative performance of the different numerical wave tank experiments was carried out on the basis of the hydrostatic pressure and wave surface elevations. The effect of numerical dissipation with the different kernel functions was also studied on the basis of energy analysis. Finally, the observations and results were used to arrive at the best possible numerical set up for simulation of waves at medium and long distances of propagation, which can play a significant role in the study of extreme waves and energy localizations observed in oceans through such numerical wave tank simulations.

Analysis of transient wave propagation in inhomogeneous media using edge-based gradient smoothing technique and bathe time integration method

As is known to all, the classical finite element method (FEM) always fails to effectively solve the wave problems in the relatively large wave numbers due to the troublesome numerical error issue. In this paper, the standard FEM with edge-based gradient smoothing technique and Bathe time integration method is developed to analyze the transient wave propagation problems in inhomogeneous media. We explicitly show that the numerical error of the calculated solutions for transient wave propagation problems consists of two different parts, namely the spatial discretization error and the temporal discretization error. Due to the edge-based gradient smoothing technique and the appropriate numerical dissipation effects from Bathe time integration scheme, it is found that the total numerical error can be significantly suppressed and more accurate numerical solutions can be obtained. Several typical numerical examples have been conducted to examine the capacity of the proposed method in solving transient wave propagation problems in inhomogeneous media.

Reduced conservation error of kinetic energy using a Runge-Kutta algorithm with reduced numerical dissipation

This paper describes an approach that reduces the error in the conservation law of velocity fluctuation intensities and turbulent kinetic energy resulting from a numerical analysis of incompressible flow. The optimized fourth-order Runge-Kutta method used to analyze acoustic problems in previous studies was used here to reduce the numerical dissipation. In order to strictly validate the conservation law of velocity fluctuation intensities and turbulent kinetic energy, the authors used a periodic box filled with an inviscid flow, where velocity fluctuation intensities and turbulent kinetic energy could be analytically held. By using the optimized Runge-Kutta method, the numerical dissipation, which is the error in conservation laws, is of the order of 1/100. The reduction in the numerical dissipation shown in this study increased with an increasing time increment. To investigate the effect of numerical dissipation, higher-order statistics of turbulent kinetic energy were calculated. This study also derived a simple mathematical form to estimate the conservation error of higher-order statistics for turbulent kinetic energy.

Numerical Investigation for Separation Characteristics of Transonic Shock Oscillations Based on Parallel Computing

Shock-induced oscillation is transonic flow instability phenomenon, which brings additional vibration to the aircraft. In this study, the RANS-LES methods with parallel computing were applied to investigate the transonic shock oscillations over a supercritical airfoil. The third-order MUSCL and fifth-order WENO based Roe scheme with adjustable dissipation were applied to study the effects of numerical dissipation. The results shown the numerical dissipation of the spatial schemes has a great influence on the calculation, and the small scale flow structure are suppressed by excessive numerical dissipation. The numerical results present the separation evolution on the upper surface. And periodic variation characteristics of the separation region downstream of the shock wave was discussed. The ratio of the time taken by the shock moves downstream and upstream is 1:1.

Transient Wave Propagation Dynamics with Edge-Based Smoothed Finite Element Method and Bathe Time Integration Technique

In this work, the edge-based smoothed finite element method (ES-FEM) is incorporated with the Bathe time integration scheme to solve the transient wave propagation problems. The edge-based gradient smoothing technique (GST) can properly soften the “overly soft” system matrices from the standard finite element approach; then, the spatial numerical dispersion error of the calculated solutions for wave problems can be significantly reduced. To effectively solve the transient wave propagation problems, the Bathe time integration scheme is employed to perform the involved time integration. Due to the appropriate “numerical dissipation effects” from the Bathe time integration method, the spurious oscillations in the relatively large wave numbers (high frequencies) can be effectively suppressed; then, the temporal numerical dispersion error in the calculated solutions can also be notably controlled. A number of supporting numerical examples are considered to examine the capabilities of the present approach. The numerical results show that ES-FEM works very well with the Bathe time integration technique, and much more numerical solutions can be reached for solving transient wave propagation problems compared to the standard FEM.

A method of adaptively adjusting dissipation for the simulation of separated flow

Separate flow is a typical complex turbulent phenomenon. The full development of small-scaled structures is of great importance for accurate numerical simulation. However, these small-scaled structures can be easily damped by the inherent dissipation of numerical method. Therefore, based on the 5th-order dissipative compact scheme (DCS), we propose an adaptive dissipative compact scheme (ADCS), which can adjust the numerical dissipation with self-adaptive capability by incorporating a flow related adjusting parameter. Combining with the delay detached eddy simulation (DDES), the ADCS can reduce the influence of numerical dissipation in LES region to enhance the ability to discern small-scaled structures, and restore the normal dissipation level in the RANS region to keep numerical stability. In the process of numerical simulation, firstly, the approximate dispersion relation (ADR) is obtained, it shows that the ADCS method can effectively reduce the influence of dissipation in the high wave number region, without contaminating the dispersive performance, which is conducive to enhancing the resolution of turbulent structures. Secondly, the advection of vortical structure is simulated. Compared with DCS, the ADCS can reach the theoretical accuracy in an efficient way and acquire more advanced resolution of vortical structure even on a relatively coarse mesh scale, which proves that the ADCS reduces the negative influence of dissipation on vortical structure. The third case is the decay of isotropic turbulence. The energy spectral curves stay close to the reference before cut-off number, showing that more small-scaled structures can be distinguished by the ADCS method, and most of the vortical dominated regions are solved at a near-minimum level. The forth case is the plate channel turbulent flow. Both of DCS method and ADCS method give acceptable results. The ADCS method is performed with optimal dissipation in the near-wall region and reduces the dissipative level in the vortex dominated region, and it is also exhibited that the ADCS method can maintain the stability for flow with high gradient and avoid divergence. Finally, the sub-critical <i>Re</i> = 3900circular cylinder is simulated, and the fully separate flow is developed in the wake. The turbulent fluctuation near the wall is sensitive to the effect of numerical dissipation. The contour of flow field shows that the ADCS method obtains more small-scale structures. As for the pressure coefficient and mean velocity, the ADCS method shows an acceptable accuracy. Considering the Reynolds stress profile, which can be easily affected by the dissipation, the ADCS exhibits more accurate results than the traditional DCS method. Generally, the ADCS method can reduce the influence of dissipation and is beneficial to acquiring more accurate results in separate flow.

A simple method of depressing numerical dissipation effects during wave simulation within the Euler model

Numerical wave tanks are widely-acknowledged tools in studying waves and wave-structure interactions. They can generate waves under realistic scales and offers more information on the fluid field. However, most numerical wave tanks suffer from issues known as the numerical dissipation and numerical dispersion. The former causes wave energy to be slowly dissipated and the latter shifts wave frequencies during wave propagation. This paper proposes a simple method of depressing numerical dissipation effects on the basis of solving Euler equations using the finite difference method (FDM). The wave propagation solutions are solved analytically taking into account the influence of the damping terms. The main idea of the method is to append a source term to the momentum equation, whose strength is determined by how strong the numerical damping effect is. The method is verified by successfully depressing numerical effects during the simulation of regular linear waves, Stokes waves and irregular waves. By applying the method, wave energy is able to be close to its initial value after long distance of travel.

Numerical symmetry-preserving techniques for low-dissipation shock-capturing schemes

Modern applications of computational fluid dynamics involve complex interactions across scales such as shock interactions with turbulent structures and multiphase interfaces. Such phenomena, which occur at very small physical viscosity, require high-resolution and low-dissipation compressible flow solvers. Many recent publications have focused on the design of high-order accurate numerical schemes and provide e.g. weighted essentially non-oscillatory (WENO) stencils up to 17th order for this purpose. As shown in detail by different authors, such schemes tremendously decrease adverse effects of numerical dissipation. However, such schemes are prone to numerically induced symmetry breaking which renders validation for the targeted problem range problematic.In this paper, we show that symmetry-breaking relates to vanishing numerical viscosity and is driven systematically by algorithmic floating-point effects which are no longer hidden by numerical dissipation. We propose a systematic procedure to deal with such errors by numerical and algorithmic formulations which respect floating-point arithmetic. We show that by these procedures inherent symmetries are preserved for a broad range of test cases with high-order shock-capturing schemes in particular in the high-resolution limit for both 2D and 3D.

Effects of numerical dissipation on the predictive accuracy of wall-modelled large-eddy simulation

The effect of numerical dissipation on the predictive accuracy of wall-modelled large-eddy simulation is investigated via systematic simulations of fully-developed turbulent channel flow. A total of 16 simulations are conducted using the open-source computational fluid dynamics software OpenFOAM®. Four densities of the computational mesh are considered, with four simulations performed on each, in turn varying in the amount of numerical dissipation introduced by the numerical scheme used for interpolating the convective fluxes. The results are compared to publicly-available data from direct numerical simulation of the same flow. Computed error profiles of all the considered flow quantities are shown to vary monotonically with the amount of dissipation introduced by the numerical schemes. As expected, increased dissipation leads to damping of high-frequency motions, which is clearly observed in the computed energy spectra. But it also results in increased energy of the large-scale motions, and a significant over-prediction of the turbulent kinetic energy in the inner region of the boundary layer. On the other hand, dissipation benefits the accuracy of the mean velocity profile, which in turn improves the prediction of the wall shear stress given by the wall model. Thus, in the current framework, the optimal choice for the dissipation of the numerical schemes may depend on the primary quantity of interest for the conducted simulation. With respect to the resolution of the grid, the change in the accuracy is much less predictable, and the optimal resolution depends on the considered quantity and the amount of dissipation introduced by the numerical schemes.

An improved discrete velocity method (DVM) for efficient simulation of flows in all flow regimes

In this paper, an improved discrete velocity method (DVM) is developed for efficient simulation of fluid problems in all flow regimes. Compared with the conventional explicit DVM, the present scheme could effectively remove its drawbacks of low accuracy and efficiency in continuum flow regime with no deterioration of its performance in rarefied flow regime. One of the novel strategies adopted in the new method is to introduce a prediction step for solving the macroscopic governing equation. By using the prediction step, the equilibrium state is first estimated before solving the discrete velocity Boltzmann equation (DVBE). As a result, the collision term in the DVBE can be discretized implicitly to improve the stability and efficiency of the conventional explicit DVM. Another contribution of the new method is to physically reconstruct numerical flux at the cell interface by incorporating the collision effect into the process. To maintain simplicity and efficiency of the conventional DVM, in the present scheme, the collision effect in the flux reconstruction at the cell interface is considered through the solution of the macroscopic governing equation. This can effectively control the effect of numerical dissipation in the process of updating the macroscopic flow variables in the continuum flow regime. Analyses indicate that the prediction step does not contribute to the evolution of distribution functions in the highly rarefied flow regime while dominating the solutions in the continuum flow regime. Accordingly, the improved scheme automatically converges toward the conventional explicit DVM in the free molecular flow regime and approaches the Navier-Stokes solver in the continuum flow regime.

Lagrangian numerical methods for ocean biogeochemical simulations

We propose two closely-related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the Péclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection–reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.

Numerical Investigation of Flow Around a Multi-Element Airfoil with Hybrid RANS-LES Approaches Based on SST Model

AbstractAccurate prediction of the flow around multi-element airfoil is a prerequisite for improving aerodynamic performance, but its complex flow features impose high demands on turbulence modeling. In this work, delayed detached-eddy-simulation (DDES) and zonal detached-eddy-simulation (ZDES) was applied to simulate the flow past a three-element airfoil. To investigate the effects of numerical dissipation of spatial schemes, the third-order MUSCL and the fifth-order interpolation based on modified Roe scheme were implemented. From the comparisons between the calculations and the available experimental result, third-order MUSCL-Roe can provide satisfactory mean velocity profiles, but the excessive dissipation suppresses the velocity fluctuations level and eliminates the small-scale structures; DDES cannot reproduce the separation near the trailing edge of the flap which lead to the discrepancy in mean pressure coefficients, while ZDES result has better tally with the experiment.

Investigation of Numerical Effects on the Flow and Combustion in LES of ICE

This work investigates the influence of numerical dissipation on the modeled combustion in Large Eddy Simulations (LES). It is well known that capturing the dynamics of the in-cylinder flow is crucial for engine simulations, as it strongly affects flame propagation. The flame propagation during the power-stroke highly depends on the turbulence level that is developed throughout compression. This turbulence level will be strongly influenced by the accuracy of the numerical schemes employed. Even a small extent of upwinding, filtering, low-order implicit time-stepping, cell-stretching or mapping between grids may affect the flow field, the turbulence level, and hence the turbulent flame speed and the pressure curve. To provide a reference, the LES in-house code PsiPhi is used, which ensures a minimum of dissipation due to high order explicit time-stepping, homogeneous and isotropic filters and cells. Good stability of the code permits the use of a second-order Central Differencing Scheme (CDS) for the transport of momentum, avoiding numerical dissipation. To analyse the effect of numerical dissipation, simulations of a fired engine are performed using different numerical schemes for the convection of momentum. Physical quantities including the total kinetic energy, the velocity gradient, the turbulent viscosity, the in-cylinder pressure, the flame propagation or the burning rate of different test cases are evaluated and compared to each other to show the numerical effects on combustion. Furthermore, the suitability of common LES quality criteria including an energy criterion and viscosity ratio is discussed based on the comparison of simulations with less and more accurate numerics. It is shown that these LES quality indicators can be highly misleading.

Effects of numerical dissipation on the interpretation of simulation results in computational fluid dynamics

Abstract The accuracy of direct and large-eddy simulations (DNS and LES) is typically assessed through a time consuming process of multiple runs and comparisons with available benchmark data. The goal is to achieve physically representative results by minimizing truncation errors in DNS, along with subgrid-scale modeling errors when performing LES. We show that even if these errors cannot be neglected, the physical accuracy can be improved if the numerical dissipation is properly accounted for in interpreting the results. Based on the balance of kinetic energy proposed by Schranner et al. [21], the method allows to compute the numerical dissipation rate and the numerical viscosity at each time step in a simulation for an arbitrary computational fluid dynamics (CFD) solver. We demonstrate that the quantitative knowledge of the numerical dissipation can be employed to better understand results obtained using dissipative CFD codes. We consider two different cases: DNS for a weakly turbulent wake past a sphere at R e = 1000 performed using the OpenFOAM solver, and LES of a laminar separation bubble flow at R e = 100 , 000 performed using a compact difference solver with stabilizing filters. The procedure is used to show that results of nominally under-resolved DNS (UDNS) can be re-interpreted as corresponding to LES results or to DNS results but for a different, effective Reynolds number that accounts for the total dissipation, consisting of the numerical dissipation and of the viscous dissipation. In both cases, comparison with benchmark data is much improved compared with cases when the nominal values used in the code are employed.

A quantification method for numerical dissipation in quasi-DNS and under-resolved DNS, and effects of numerical dissipation in quasi-DNS and under-resolved DNS of turbulent channel flows

LES for industrial applications with complex geometries is mostly characterised by: a) a finite volume CFD method using a non-staggered arrangement of the flow variables and second order accurate spatial and temporal discretisation schemes, b) an implicit top-hat filter, where the filter length is equal to the local computational cell size, and c) eddy-viscosity type LES models. LES based on these three main characteristics is indicated as industrial LES in this paper.It becomes increasingly clear that the numerical dissipation in CFD codes typically used in industrial applications with complex geometries may inhibit the predictive capabilities of explicit LES. Therefore, there is a need to quantify the numerical dissipation rate in such CFD codes. In this paper, we quantify the numerical dissipation rate in physical space based on an analysis of the transport equation for the mean turbulent kinetic energy. Using this method, we quantify the numerical dissipation rate in a quasi-Direct Numerical Simulation (DNS) and in under-resolved DNS of, as a basic demonstration case, fully-developed turbulent channel flow. With quasi-DNS, we indicate a DNS performed using a second order accurate finite volume method typically used in industrial applications. Furthermore, we determine and explain the trends in the performance of industrial LES for fully-developed turbulent channel flow for four different Reynolds numbers for three different LES mesh resolutions. The presented explanation of the mechanisms behind the observed trends is based on an analysis of the turbulent kinetic energy budgets.The presented quantitative analyses demonstrate that the numerical errors in the industrial LES computations of the considered turbulent channel flows result in a net numerical dissipation rate which is larger than the subgrid-scale dissipation rate.No new computational methods are presented in this paper. Instead, the main new elements in this paper are our detailed quantification method for the numerical dissipation rate, the application of this method to a quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow, and the explanation of the effects of the numerical dissipation on the observed trends in the performance of industrial LES for fully-developed turbulent channel flows.

Effective and energy-preserving time discretization for a general nonlinear poromechanical formulation

We consider a general nonlinear poromechanical model, formulated based on fundamental thermodynamics principle, suitable for representing the coupling of rapid internal fluid flows with large deformations of the solid, and compatible with a wide class of constitutive behavior. The objective of the present work is to propose for this model a time discretization scheme of the partitioned type, to allow the use of existing time schemes – and possibly separate solvers – for each component of the model, i.e. for the fluid and the solid. To that purpose, we adapt and extend an earlier proposed approach devised for fluid-structure interaction in an Arbitrary Lagrangian-Eulerian framework. We then establish an energy estimate for the resulting time scheme, in a form that is consistent with the underlying energy principle in the poromechanical formulation, up to some numerical dissipation effects and some perturbations that we have carefully identified and assessed. In addition, we provide some numerical illustrations of our numerical strategy with test problems that present typical features of large strains and rapid fluid flows, and also a case of singular transition related to total drainage. An example of challenging application envisioned for this model and associated numerical coupling scheme concerns the perfusion of the heart.

A priori and a posteriori evaluations of sub-grid scale models for the Burgers’ equation

Abstract In large eddy simulations (LES) of turbulent flows, large scale motions are resolved by the numerical simulation while the effect of the small scale motions is represented as sub-grid scale (SGS) stresses computed with SGS models. In the present study, we perform a priori and a posteriori evaluations of five SGS models for the one dimensional Burgers’ equation with the high-order flux reconstruction (FR) or correction procedure via reconstruction (CPR) approach. It is shown that all models, except the scale similarity model (SSM) and the mixed model (MM), demonstrate very little correlation with the DNS results. The stability of the SSM is investigated. The effects of numerical dissipation and the models’ influence on LES are discussed. Based on the present study, we advocate the use of implicit LES (ILES) in LES in the context of discontinuous high-order methods, or any numerical methods with built-in numerical dissipation.

On the Advection-Upstream-Splitting-Method Hybrid Scheme: A Simple Transient-Flow Model for Managed-Pressure-Drilling and Underbalanced-Drilling Applications

Summary Transient flow models play an important role in the planning and follow-up of advanced well operations such as managed pressure drilling (MPD) and underbalanced operations. The most recent trend is a situation whereby flow models and control-engineering algorithms are combined in various settings to control flow parameters. This requires robust flow models and an in-depth understanding of uncertainties in the modeling process. This paper presents a simple and robust transient model that can handle highly dynamic flow systems. The model, the Advection-Upstream-Splitting-Model hybrid scheme, was developed for academic and training purposes. With the model, students can investigate different flow scenarios and pressure-control challenges encountered in general well control, MPD, underbalanced drilling, and automation. The capability of this model to handle highly changing flow scenarios is demonstrated with examples taken from MPD and underbalanced operations. The effect of numerical dissipation on the model predictions is briefly discussed.

Large eddy simulation requirements for the Richtmyer-Meshkov instability

The shock induced mixing of two gases separated by a perturbed interface is investigated through Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). In a simulation, physical dissipation of the velocity field and species mass fraction often compete with numerical dissipation arising from the errors of the numerical method. In a DNS, the computational mesh resolves all physical gradients of the flow and the relative effect of numerical dissipation is small. In LES, unresolved scales are present and numerical dissipation can have a large impact on the flow, depending on the computational mesh. A suite of simulations explores the space between these two extremes by studying the effects of grid resolution, Reynolds number, and numerical method on the mixing process. Results from a DNS are shown using two different codes that use a high- and low-order numerical method and show convergence in the temporal and spectral dependent quantities associated with mixing. Data from an unresolved, high Reynolds number LES are also presented and include a grid convergence study. A model for an effective viscosity is proposed which allows for an a posteriori analysis of the simulation database that is agnostic to the LES model, numerics, and the physical Reynolds number of the simulation. An analogous approximation for an effective species diffusivity is also presented. This framework is then used to estimate the effective Reynolds number and Schmidt number of future simulations, elucidate the impact of numerical dissipation on the mixing process for an arbitrary numerical method, and provide guidance for resolution requirements of future calculations in this flow regime.