Adaptive Dissipation Control Research Articles

Weighted compact nonlinear scheme based on smooth scale separation for self-adaptive turbulence eddy simulations

Multiscale compressible turbulent flow is widely present in the aerospace field, and the co-existence of shock wave discontinuities and multi-scale turbulence in the flow field poses significant challenges for high-fidelity numerical simulation. To design high-order nonlinear scheme to improve the accuracy of complex turbulence simulation with stable shock wave capture, a weighted compact nonlinear scheme – targeted essentially non-oscillatory (WCNS-T) scheme is developed based on targeted essentially non-oscillatory scheme within the WCNS framework. Also, an improved variant of WCNS-T with smooth scale separation (denoted as WCNS-ST) is proposed from the perspective of both numerical convergence and accuracy. The numerical properties of different nonlinear weights are discussed in classical numerical problems, including spectral properties analysis, and two-dimensional Riemann problem. Then, the newly developed WCNS-ST scheme based on smooth scale separation was used to combine a unified turbulence model called Self-Adaptive Turbulence Eddy Simulation (SATES), which is applied to simulate subsonic flow past a 30P30N airfoil and supersonic base flow. The good convergence and numerical results are obtained using the newly developed WCNS-ST scheme, whereas WCNS-T shows worse convergence. In addition, adaptive dissipation control is further introduced for the WCNS-ST scheme, and the new variant (denoted as WCNS-STA) still shows good residual convergence and predicts more accurate results due to low numerical dissipation. The above results indicate that the proposed smooth scale separation and its WCNS-STA scheme have a good performance in SATES simulations of multiscale flow problems, making it more potential for complex engineering applications.

Adaptive numerical dissipation control for high-order k-exact reconstruction schemes on vertex-centered unstructured grids using artificial neural networks

Due to their enhanced numerical dissipation properties, high-order discretization methods are an important prerequisite to obtain accurate results with Large-Eddy Simulations. However, the exact amount of dissipation often requires a careful tuning by the user via problem-dependent parameters. In this work we present a fully adaptive dissipation control, which ensures stability and additionally reduces the numerical dissipation to a minimum. This novel approach employs a simple feedforward neural network model, which indirectly tabulates an underlying stability equation and thus reduces the computational overhead to estimate the dissipation during runtime. The methodology is adapted for a high-order k-exact reconstruction method on fully unstructured vertex-centered grids, and it is implemented in a full production flow solver. Based on several test cases, the enhanced accuracy compared to a conventional low-order scheme is demonstrated. Especially when dealing with Large-Eddy Simulation benchmarks, significant savings in computation time and grid resolution requirements can be obtained for reaching a desired level of accuracy. Moreover, compared to a high-order reconstruction method with constant numerical dissipation, the presented adaptive approach consistently yields accurate results, regardless of the flow problem.

Very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control

In this paper, a new family of very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control (TENO-AA) is proposed. The new framework allows for constructing arbitrarily high-order TENO schemes in a unified paradigm and the yielded nonlinear schemes gradually reduce to low-order reconstructions by judging the smoothness with the ENO-like stencil selection strategy. In order to control the nonlinear numerical dissipation adaptively, the flow scales are first measured by examining the first-order undivided difference and the cut-off constant CT in the TENO weighting strategy is adapted based on the corresponding measurement. With one set of optimal parameters, the newly proposed TENO schemes are designed to deliver excellent performance for predicting highly compressible flows with a wide range of Mach numbers. While the new very-high-order TENO schemes feature good robustness for conventional gas dynamics, the ENO-property is well preserved with the assistant of a positivity-preserving flux limiter for extreme simulations. Without loss of generality, the typical eight- and ten-point TENO-AA schemes are constructed. A set of benchmark simulations are computed to demonstrate the performance of the proposed TENO schemes.

Three novel truly-explicit time-marching procedures considering adaptive dissipation control

In this paper, three novel truly-explicit time-marching techniques are proposed for the solution of hyperbolic models. In these techniques, locally computed time-integration parameters are applied, which are defined taking into account the properties of the spatially/temporally discretised model and the evolution of the computed responses. These adaptive time integrators allow introducing enhanced numerical damping into the analysis, reducing spurious non-physical oscillations that occur due to the excitation of spatially unresolved modes. The proposed adaptive techniques are formulated based on second-, third-, and fourth-order accurate time-marching approaches, providing solution algorithms with different complexities. At the end of the paper, numerical results are presented, illustrating the good performance of the proposed procedures.

High order nonlinear filter methods for subsonic turbulence simulation with stochastic forcing

Numerical simulations of forced turbulence in compressible fluids are challenging due to the multi-scale nature of the problem and conflicting requirements for numerical methods to accurately resolve the small scales and, at the same time, to handle shock waves and other discontinuities without generating spurious oscillations. Minimizing nonlinear instability and aliasing error while maintaining high accuracy before the simulation reaches the statistically stationary stage is computationally intensive. The goal of this work is to employ an efficient class of high order finite difference nonlinear filter methods for subsonic turbulence simulation with stochastic forcing. The 3D Euler equations for subsonic turbulence with temporally varying stochastic forcing at rms Mach numbers up to 0.6 are numerically solved using the Strang operator splitting of the homogeneous part of the Euler equations and the forcing terms. It was shown in Yee et al. (2013) that the Strang operator splitting is more stable than solving the full Euler equation with the source term included. The spatially seventh-order nonlinear filter methods with adaptive dissipation control developed by Yee & Sjögreen (2007, 2011) are used to solve the homogeneous system and an ODE solver is used to solve the forcing source terms. The nonlinear filter method includes a full time step of a spatially eighth-order central base method, using a third-order TVD Runge-Kutta time integration. The solution computed with the central base method is then nonlinearly filtered by an adaptive flow sensor and the dissipative portion of a seventh-order WENO with the Roe Riemann solver. In order to improve nonlinear stability of the base method without added numerical dissipation, the central base method discretizes the skew-symmetric split form of the inviscid flux derivatives. Both Ducros et al. and Kennedy-Gruber skew-symmetric split forms are tested. Numerical stability, computational efficiency, and effective spectral bandwidth of the nonlinear filter schemes are compared with those of second-order TVD and fifth- and seventh-order WENO methods. It is shown that the nonlinear filter method for this application is substantially more efficient, accurate and yields a superior spectral bandwidth compared to the standard TVD and WENO methods. The nonlinear filter method also demonstrates robust long-time integration for moderately compressible, statistically stationary turbulence with large-scale solenoidal forcing, including small-scale quantities such as enstrophy and mean-square dilatation.

Comparative study of high order methods for subsonic turbulence simulation with stochastic forcing

A class of spatially seventh-order nonlinear filter methods with adaptive dissipation control developed by Yee & Sjögreen [1, 2] is tested on three-dimensional subsonic turbulence simulations with stochastic forcing. The Euler equations are solved using the Strang operator splitting of the homogeneous part of the equations and the stochastic forcing term, with an ODE solver used to integrate the latter. Both Ducros et al. and Kennedy-Gruber skew-symmetric split formulations of the inviscid flux derivatives are considered to minimize the use of numerical dissipation. The nonlinear filter methods are shown to be numerically stable for this application at least up to an rms Mach number of 0.6. The performance and accuracy of this numerical approach are compared with those of second order TVD and fifth and seventh order WENO methods. The nonlinear filter methods are shown to be substantially more computationally efficient, delivering a superior spectral bandwidth compared to the standalone TVD and WENO methods.

A simple extended compact nonlinear scheme with adaptive dissipation control

Weighted compact nonlinear schemes (WCNSs) [1] are a popular family of high resolution shock-capturing methods, of which the nonlinear interpolation procedure is essential for non-oscillatory shock-capturing computation. In this article, numerical dissipation of an improved compact nonlinear scheme, which is fifth-order accurate, is significantly reduced by further introducing a six-point optimized stencil in the nonlinear interpolation, without using more complex local or global smoothness indicators. Nonlinear dissipation and dispersion are then further reduced by using an adaptive strategy. In particular, the computational procedure including the proposed six-point nonlinear interpolation is almost the same as that of the improved five-point scheme, and thus their computational efforts are similar. However, significant gains in numerical performance are obtained while including the six-point optimized stencil. Benchmark cases in one and two space dimensions are used to assess performance of the present scheme, viz., shock-capturing capability and resolution in smooth regions, showing promising advantages.

A DC fault ride‐through and energy dissipation scheme for hybrid MMC‐MTDC integrating wind farms with overhead lines

To integrate bulk wind power, using modular multilevel converter (MMC) based DC grids is an effective solution to improve the flexibility and reliability of the power grid. This paper analyses a bipolar four-terminal MMC based DC grid to integrate wind farms with overhead lines. Since the overhead lines are prone to DC faults, the hybrid MMC is adopted in the system to ride through DC faults. The fault ride-through control strategies are designed, which remain continuous operation of wind turbines under DC faults. Besides, an adaptive dissipation control strategy associated with chopper resistances is designed to absorb surplus energy. Finally, simulations based on PSCAD/EMTDC platform verify the fault ride through control of hybrid MMC based DC grid and proves the effectiveness of the energy dissipation strategies.

An implicit family of time marching procedures with adaptive dissipation control

In this work, an unconditionally stable family of time marching procedures is proposed, in which the time integration parameters of the method are locally computed, considering the properties of the model. Thus, the technique adapts to the characteristics of the problem, enabling enhanced analyses. Here, adaptive dissipation control is explored, allowing spurious modes to be more effectively dissipated. The proposed technique is second-order accurate, L-stable, truly self-starting and very easy to implement. Numerical results are presented along the paper, illustrating the good performance of the novel single-step technique.

An explicit family of time marching procedures with adaptive dissipation control

SUMMARYIn this work, an explicit family of time marching procedures with adaptive dissipation control is introduced. The proposed technique is conditionally stable, second‐order accurate, and has controllable algorithm dissipation, which adapts according to the properties of the governing system of equations. Thus, spurious modes can be more effectively dissipated and accuracy is improved. Because this is an explicit time integration technique, the new family is quite efficient, requiring no system of equations to be dealt with at each time step. Moreover, the technique is simple and very easy to implement. Numerical results are presented along the paper, illustrating the good performance of the proposed method, as well as its potentialities. Copyright © 2014 John Wiley & Sons, Ltd.