Dissipative Numerical Scheme Research Articles

Simulation of the Laminar–Turbulent Transition by Applying Dissipative Numerical Schemes

The applicability of a low-order monotone shock-capturing scheme to the simulation of the laminar–turbulent transition is demonstrated. The laminar–turbulent transition is simulated in a supersonic boundary layer over a flat plate at a Mach number of 3. The numerical results are compared with results of other authors based on low-dissipative schemes. The spectral characteristics of disturbances in the linear and nonlinear development regions, the structure of the transient flow, and averaged boundary layer characteristics are compared.

Numerical investigation towards the improvement of hydraulic-jump prediction in rectangular open-channels

ABSTRACT This study probed into the numerical characterization of a rapidly varied free-surface flow behavior including a hydraulic jump onset. The extended One-Dimensional St.-Venant Equations, embedding the Boussinesq add-on term, were employed to describe a free-surface wave behavior. The numerical computations were based on a second-order precision in time and fourth-order in space explicit finite-difference scheme ((2/4)-dissipative numerical scheme). The computed results were then compared with those issued from the McCormack – based alternative solver and experimental data quoted in the literature. The findings revealed that the developed solver allowed an accurate prediction of the amplitude and location characteristics of the hydraulic jump. In addition, they suggested that the (2-4)-dissipative scheme-based algorithm was more practical than the alternative shock capturing methods in terms of prediction accuracy, implementation simplicity, and calculation time consumption. Unlike the McCormack scheme – based solver, the proposed algorithm provided numerical signals free of numerical oscillations in the vicinity of the steep gradient involved by hydraulic jumps. Yet, it required more computational time than the McCormack scheme – based alternative.

Dissipative Numerical Schemes on Riemannian Manifolds with Applications to Gradient Flows

This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differen...

Energy dissipative numerical schemes for gradient flows of planar curves

In this paper, we develop an energy dissipative numerical scheme for gradient flows of planar curves, such as the curvature flow and the elastic flow. Our study presents a general framework for solving such equations. To discretize the time variable, we use a similar approach to the discrete partial derivative method, which is a structure-preserving method for gradient flows of graphs. For the approximation of curves, we use B-spline curves. Owing to the smoothness of B-spline functions, we can directly address higher order derivatives. Moreover, since B-spline curves require few degrees of freedom, we can reduce the computational cost. In the last part of the paper, we present some numerical examples of the elastic flow, which exhibit topology-changing solutions and more complicated evolution. Videos illustrating our method are available on YouTube.

Three-dimensional shock wave configurations induced by two asymmetrical intersecting wedges in supersonic flow

This study explores the three-dimensional (3D) wave configurations induced by 3D asymmetrical intersecting compression wedges in supersonic and hypersonic inviscid flows. By using the “spatial dimension reduction” approach, the problem of 3D steady shock/shock interaction is converted to that of the interaction of two moving shock waves in the characteristic two-dimensional (2D) plane. Shock polar theory is used to analyze the shock configurations in asymmetrical situations. The results show that various shock configurations exist in 3D asymmetrical shock wave interactions, including regular interaction, transitioned regular interaction, single Mach interaction, inverse single Mach interaction, transitional double Mach interaction, weak shock interaction, and weak single Mach interaction. All of the above 3D steady shock/shock interactions have their corresponding 2D moving shock/shock interaction configurations. Numerical simulations are performed by solving the 3D inviscid Euler equations with the non-oscillatory, non-free parameters, dissipative (NND) numerical scheme, and good agreement with the theoretical analysis is obtained. Furthermore, the comparison of results show that the concept of the “virtual wall” in shock dynamics theory is helpful for understanding the mechanism of two-dimensional shock/shock interactions.

Numerical simulations of separated flows at moderate Reynolds numbers appropriate for turbine blades and unmanned aero vehicles

Flows over airfoils and blades in rotating machinery, for unmanned and micro-aerial vehicles, wind turbines, and propellers consist of a laminar boundary layer near the leading edge that is often followed by a laminar separation bubble and transition to turbulence further downstream. Typical RANS turbulence models are inadequate for such flows. Direct numerical simulation (DNS) is the most reliable, but is also the most computationally expensive alternative. This work assesses the capability of Immersed Boundary (IB) methods and Large Eddy Simulations (LES) to reduce the computational requirements for such flows and still provide high quality results. Two-dimensional and three-dimensional simulations of a laminar separation bubble on a NACA-0012 airfoil at Rec=5×104 at 5° of incidence have been performed with an IB code and a commercial code using body fitted grids. Several Subgrid Scale (SGS) models have been implemented in both codes and their performance evaluated. For the two-dimensional simulations with the IB method the results show good agreement with DNS benchmark data for the pressure coefficient Cp and the friction coefficient Cf but only when using dissipative numerical schemes. There is evidence that this behavior can be attributed to the ability of dissipative schemes to damp numerical noise coming from the IB. For the three-dimensional simulations the results show a good prediction of the separation point, but inaccurate prediction of the reattachment point unless full DNS resolution is used. The commercial code shows good agreement with the DNS benchmark data in both two and three-dimensional simulations, but the presence of significant, unquantified numerical dissipation prevents a conclusive assessment of the actual prediction capabilities of very coarse LES with low order schemes in general case.

Towards the development of a robust model hierarchy: investigation of dynamical limitations at low resolution and possible solutions

AbstractIn order to investigate questions concerning changes in the atmosphere and other components of the Earth system, it is desirable to have a seamless modelling system that operates across a wide range of time‐scales and horizontal resolutions. The development of a low‐resolution configuration of the model would greatly assist in addressing these scientific questions whose long time‐scales or complexity are computationally demanding—a cost that cannot be sustained by higher resolutions. However, in order to be confident that results remain robust to changes in resolution, it is essential that such models include the same underlying fundamental processes as those at higher resolution.Some resolution‐dependent biases are found to grow (notably when horizontal resolution decreases below ∼150 km) as a result of the lack of transient eddy kinetic energy (TEKE). The advection scheme used by many of the current general circulation models follows the semi‐Lagrangian (SL) dynamics approach. Because of the need for interpolation to the departure point, the scheme is highly diffusive when low‐order interpolation schemes are used. We analyse how the impact of the high diffusivity of SL schemes leads to a lack of TEKE, which inhibits the development of mid‐latitude variability phenomena such as synoptic cyclones or blocking events. Conversely, some examples where the performance of the low resolution is acceptable are provided.We investigate two different traceable solutions to partially offset the misrepresentation of dynamical features in the low‐resolution version: a change of the interpolation scheme from quasi‐cubic to quintic interpolation; and vorticity confinement: a parametrization designed to preserve vorticity features in dissipative numerical schemes. Both solutions are found to increase TEKE and improve many of the mid‐latitude metrics considered. Copyright © 2012 British Crown copyright, the Met Office. Published by John Wiley & Sons Ltd.

Modified kinetic flux vector splitting (m-KFVS) method for compressible flows

To resolve many flow features accurately, like accurate capture of suction peak in subsonic flows and crisp shocks in flows with discontinuities, to minimise the loss in stagnation pressure in isentropic flows or even flow separation in viscous flows require an accurate and low dissipative numerical scheme. The first order kinetic flux vector splitting (KFVS) method has been found to be very robust but suffers from the problem of having much more numerical diffusion than required, resulting in inaccurate computation of the above flow features. However, numerical dissipation can be reduced by refining the grid or by using higher order kinetic schemes. In flows with strong shock waves, the higher order schemes require limiters, which reduce the local order of accuracy to first order, resulting in degradation of flow features in many cases. Further, these schemes require more points in the stencil and hence consume more computational time and memory. In this paper, we present a low dissipative modified KFVS (m-KFVS) method which leads to improved splitting of inviscid fluxes. The m-KFVS method captures the above flow features more accurately compared to first order KFVS and the results are comparable to second order accurate KFVS method, by still using the first order stencil.

Hybrid Particle-Continuum Simulations of Hypersonic Flow Over a Hollow-Cylinder-Flare Geometry

A modular particle-continuum numerical method is used to simulate steady-state hypersonic flow over a hollow-cylinder-flare geometry. The resulting flowfield involves a mixture of rarefied nonequilibrium flow and high-density continuum flow. The hybrid particle-continuum method loosely couples direct simulation Monte Carlo and Navier-Stokes methods, which operate in different regions, use different mesh densities, and are updated using different-sized time steps. Hybrid numerical results are compared with full particle and full continuum simulations as well as with experimental data. The hybrid particle-continuum simulations are demonstrated to reproduce experimental and full particle simulation results for surface and flowfield properties including velocity slip, temperature jump, thermal nonequilibrium, heating rates, and pressure distributions with high accuracy. The hybrid method, which uses particle simulation next to the surface, is also shown to predict accurate heating rates even when a highly dissipative numerical scheme is used for the continuum solver. For this particular flow, a hybrid simulation is obtained with modest computational savings over full particle simulation.

Effective eddy viscosities in implicit large eddy simulations of turbulent flows

We propose a method for computing effective numerical eddy viscosity acting in dissipative numerical schemes used in monotonically integrated large eddy simulations of turbulence. The method is evaluated on an example of a specific nonoscillatory finite volume scheme MPDATA developed for simulations of geophysical flows.