Benchmark Test Cases Research Articles

A Novel Hybrid Approach Based on Cellular Automata and a Digital Elevation Model for Rapid Flood Assessment

An efficient inundation model is necessary for emergency flood responses during storm events. Cellular automata (CA)-based flood models have been proven to produce rapid results while maintaining a certain degree of accuracy. However, the need for computational resources dramatically increases when the number of grid cells increases. Digital elevation model (DEM)-based models generate results even faster, but the simplified governing equations within the models fail to reflect temporal flood evolution. To achieve rapid flood modeling while maintaining model simplicity, a novel two-dimensional hybrid inundation model (HIM) was developed by combining the CA- and DEM-based concepts. Given the temporal flood evolution generated by the CA concept, final finer-scale predictions were obtained by applying the DEM-based concept. The performance of this model was compared to those of widely used, physically based hydraulic models using three UK Environment Agency (EA) benchmark test cases. The HIM yielded consistent prediction results but was faster than the CA-based model. Finally, a comparison was made against flood observations, and the overall root mean squared error (RMSE) for flood depth was 0.388–0.400 m. Considering the uncertainty in the observed flood depths, the HIM shows promising potential to serve as an intermediate tool for emergency response in practical cases.

Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using subcell flux corrections and convex limiting. These methods are based on a subcell flux corrected transport (FCT) methodology that involves blending a high-order target scheme with a robust, low-order invariant domain preserving method that is obtained using a graph viscosity technique. The new low-order discretizations are based on sparse stencils which do not increase with the polynomial degree of the high-order DG method. As a result, the accuracy of the low-order method does not degrade when used with high-order target methods. The method is applied to both scalar conservation laws, for which the discrete maximum principle is naturally enforced, and to systems of conservation laws such as the Euler equations, for which positivity of density and a minimum principle for specific entropy are enforced. Numerical results are presented on a number of benchmark test cases.

Convergence acceleration of iterative sequences for equilibrium chemistry computations

The modeling of thermodynamic equilibria leads to complex nonlinear chemical systems which are often solved with the Newton-Raphson method. But this resolution can lead to a non convergence or an excessive number of iterations due to the very ill-conditioned nature of the problem. In this work, we combine a particular formulation of the equilibrium system called the Positive Continuous Fraction method with two iterative methods, Anderson Acceleration method and Vector extrapolation methods (namely the reduced rank extrapolation and the minimal polynomial extrapolation). The main advantage of this approach is to avoid forming the Jacobian matrix. In addition, a strategy is used to improve the robustness of the Anderson acceleration method which consists in reducing the condition number of matrix of the least squares problem in the implementation of the Anderson acceleration so that the numerical stability can be guaranteed. We compare our numerical results with those obtained with the Newton-Raphson method on the Acid Gallic test and the 1D MoMas benchmark test case and we show the high efficiency of our approach.

Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme

We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids, also called yield-stress fluids. In contrast to the conventional approaches relying on the non-linear viscosity concept of the Navier-Stokes theory and representation of the solid state as an infinitely rigid non-deformable solid, the solid state in our theory is deformable and the fluid state is considered rather as a “melted” solid via a certain procedure of relaxation of tangential stresses similar to Maxwell’s visco-elasticity theory. The model is formulated as a system of first-order hyperbolic partial differential equations with possibly stiff non-linear relaxation source terms. The computational strategy is based on a staggered semi-implicit scheme which can be applied in particular to low-Mach number flows as usually required for flows of non-Newtonian fluids. The applicability of the model and numerical scheme is demonstrated on a few standard benchmark test cases such as Couette, Hagen-Poiseuille, and lid-driven cavity flows. The numerical solution is compared with analytical or numerical solutions of the Navier-Stokes theory with the Herschel-Bulkley constitutive model for nonlinear viscosity.

DDPG Agent to Swing Up and Balance Cart- Pole System

Reinforcement learning is a mathematical framework for agents to interact intelligently with their environment. Unlike supervised learning, where a system learns with the help of labeled data, reinforcement learning agents learn how to act by trial and error only receiving a reward signal from their environments. A field where reinforcement learning has been prominently successful is robotics [3]. However, real-world control problems are also particularly challenging because of the noise and high- dimensionality of input data (e.g., visual input). In recent years, in the field of supervised learning, deep neural networks have been successfully used to extract meaning from this kind of data. Building on these advances, deep reinforcement learning was used to solve complex problems like Atari games and Go. Mnih et al. [1] built a system with fixed hyper parameters able to learn to play 49 different Atari games only from raw pixel inputs. However, in order to apply the same methods to real-world control problems, deep reinforcement learning has to be able to deal with continuous action spaces. Discretizing continuous action spaces would scale poorly, since the number of discrete actions grows exponentially with the dimensionality of the action. Furthermore, having a parametrized policy can be advantageous because it can generalize in the action space. Therefore with this thesis we study state-of-the-art deep reinforcement learning algorithm, Deep Deterministic Policy Gradients. We provide a theoretical comparison to other popular methods, an evaluation of its performance, identify its limitations and investigate future directions of research. The remainder of the thesis is organized as follows. We start by introducing the field of interest, machine learning, focusing our attention of deep learning and reinforcement learning. We continue by describing in details the two main algorithms, core of this study, namely Deep Q-Network (DQN) and Deep Deterministic Policy Gradients (DDPG). We then provide implementatory details of DDPG and our test environment, followed by a description of benchmark test cases. Finally, we discuss the results of our evaluation, identifying limitations of the current approach and proposing future avenues of research.

Full space‐time adaptive method based on collocation strategy and implicit multirate time stepping

AbstractIn this paper, we present a full space‐time Adaptive Fup Collocation Method (AFCM) for solving initial‐boundary value problems with particular application on advection‐dominated advection‐diffusion problems. The spatial adaptive strategy dynamically changes the computational grid at each global time step, while the adaptive time‐marching algorithm uses different local time steps for different collocation points based on temporal accuracy criteria. Contrary to the existing space‐time adaptive methods that are based on explicit temporal discretization and scale‐dependent local time stepping, the presented method is implicit and resolves all spatial and temporal scales independently of each other. This means that smaller local time steps are used only for spatial zones where temporal solution changes are intensive, which are not necessarily the zones with finest spatial discretization. In this manner, the computationally efficient full space‐time adaptive strategy accurately resolves small‐scale features and controls numerical error and spurious oscillations. The efficiency and accuracy of AFCM are verified with some classical one‐ and two‐dimensional benchmark test cases.

Parameters identification of PV model using improved slime mould optimizer and Lambert W-function

The characterization of PV unit can be made using one-, two-, and triple-diode electrical model. Each model has its own merits in terms of number of unknown parameters to be extracted and burden of calculation, and etc. In most applications, one-diode model (1-DM) is sufficed for the purpose of simulation and analysis in steady-state and dynamic conditions. This paper cares of extracting the unknown five parameters of the 1-DM exploiting the real I-V dataset points. New effort of employing the slime mould algorithm (SMA) and its improved version (ImSMA) is addressed to attain the same goal. Lambert W-function or omega function is used for accurate calculus of PV current. Two benchmarking test cases widely used in the literature are demonstrated and analysed to appraise the performance of SMA/ImSMA complete with subsequent analysis and discussions. The best ImSMA’s results of root mean squared current errors are 7.73006e−4 A and 1.3798e−2 A for RTC solar cell and STP6-120/36; respectively. Various scenarios under varied conditions are demonstrated utilizing the cropped best values of the model’s parameters In addition to that, performance measures are made to validate the cropped results along with comparisons to other recent competing algorithms. It can be concluded that the validations in consort with established outcomes signify the ImSMA in recognizing the PV unidentified 1-DM parameters.

A coupled incompressible SPH-Hamiltonian SPH solver for hydroelastic FSI corresponding to composite structures

The paper presents a fully Lagrangian meshfree projection-based hydroelastic FSI (Fluid-Structure Interaction) solver for simulation of incompressible fluid flows interacting with laminated composite elastic structures. The presented computational method is configured within the SPH (Smoothed Particle Hydrodynamics) framework. An enhanced version of Incompressible SPH (ISPH) is adopted as the fluid model and a structure model in the context of Hamiltonian SPH (HSPH) is coded for stable, accurate and conservative simulations of laminated composite elastic structures. The fluid-structure coupling is conducted by either the Fluid-Structure Acceleration-based (FSA) or the Pressure Integration (PI) coupling scheme with careful considerations of interface boundary conditions and numerical stability with respect to the discontinuities in densities of constituent laminates of considered composite structures. A distinct superiority of the proposed solver corresponds to absence of any artificial stabilizers or artificial smoothing of material properties at material interfaces. Verifications are coherently performed by conducting several benchmark test cases with exact analytical solutions, first for structures and then for fluid-structure systems. Finally, to portray the potential applicability of the solver for practical engineering applications, a challenging simulation of water slamming on a sandwich hull, comprising of large discontinuities in structural material properties is conducted. To the best knowledge of authors, this paper presents the first hydroelastic FSI solver corresponding to composite structures in the context of SPH.

A reconstructed discontinuous Galerkin method for compressible flows on moving curved grids

A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving and deforming unstructured curved meshes. Taylor basis functions in the rDG method are defined on the time-dependent domain, where the integration and computations are performed. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. A radial basis function (RBF) interpolation method is used for propagating the mesh motion of the boundary nodes to the interior of the mesh. A third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) is employed for the temporal integration. A number of benchmark test cases are conducted to assess the accuracy and robustness of the rDG-ALE method for moving and deforming boundary problems. The numerical experiments indicate that the developed rDG method can attain the designed spatial and temporal orders of accuracy, and the RBF method is effective and robust to avoid excessive distortion and invalid elements near moving boundaries.

Numerical procedure for electro-thermal anti-icing system simulation coupling internal thermal analysis and external multi-physic code

The present work has the aim of coupling two codes, one able to perform icing simulations and another one capable to simulate the performance of an electro-thermal anti-icing system in an integrated fashion. In fact, the classical tool chain of icing simulation (aerodynamics, water catch and impact, mass and energy surface balance) is coupled to the thermal analysis through the surface substrate and the ice thickness. In general, the substrate consists of a multi-layered composite with different properties for each layer and embedded heaters (resistors) at interfaces between layers. In the present approach, the ice protection simulation is not decoupled from the ice accretion simulation, but a single computational workflow is considered. Validation results obtained on benchmark test cases from NASA database will be detailed as well as comparison with numerical results from other authors.

Implementation of APSO and Improved APSO on Non-Cascaded and Cascaded Short Term Hydrothermal Scheduling

Short-term hydrothermal scheduling (STHTS) is a highly non-linear, multi-model, non-convex, and multi-dimensional optimization problem that has been worked upon for about 5 decades. Many research articles have been published in solving different test cases of STHTS problem, while establishing the superiority of one type of optimization algorithm over the type, in finding the near global best solution of these complex problems. This paper presents the implementation of an improved version of a variant of the Particle Swarm Optimization algorithm (PSO), known as Accelerated Particle Swarm Optimization (APSO) on three benchmark test cases of STHTS problems. The adaptive and variable nature of the local and global search coefficients for the proposed APSO significantly improve its performance in obtaining the optimal solution for the STHTS test cases. Two of these cases are non-cascaded cases of STHTS problem (NCSTHTS) and one case is cascaded case of STHTS problem (CSTHTS). The results are compared with the results of the previous implementations of the other algorithms as presented in the literature. Due to the stochastic nature of the meta-heuristic algorithms, the parametric and non-parametric statistical tests have been implemented to establish the superiority of results of one type of algorithm over the results of the other type of algorithms.

Benchmark comparison of dual-basis double-hybrid density functional theory and a neural-network-optimized method for intermolecular interactions

We present a computationally efficient implementation of double-hybrid density functional theory (DH-DFT) leveraging the dual basis methods of Head-Gordon and co-workers and the resolution-of-the-identity second-order Møller-Plesset (RI-MP2) theory. The B2PLYP, B2GP-PLYP, DSD-BLYP and DSD-PBEP86 density functionals are applied to assess the performance of dual-basis methods on several benchmark test cases, including the CONF set of conformational energy differences in C4-C7 alkanes, the S22 set of noncovalent interaction energies, and the RGC10 noble-gas dimer dissociation curves. The dual-basis DH-DFT approach is shown to give results in excellent agreement with conventional methods at a reduced computational cost. For noncovalent interaction energies, DH-DFT is compared against a leading neural-network-based approach, namely the SNS-MP2 method of McGibbon and coworkers (McGibbon et al., 2017). The DH-DFT and SNS-MP2 methods are shown to produce similar accuracies when compared to the established benchmark values.

Simulation of Mosul Dam Break Using Finite Volume Method

Mosul dam is an earth-fill embankment located north of Iraq on the Tigris River forming a reservoir with 11.11 km3 water storage capacity which is the largest dam in the country. The dam is built on a rock bed foundation, in which the dissolution process is dynamic in the zone where gypsum and anhydrite layers present. During the construction development seepage locations were found in the dam foundation and the grouting process is in progress until now to control this problem. Therefore, the possibility of the Mosul dam break is highlighted by previous studies. In this research, a FORTRAN code based on the finite volume method is modified to solve the two-dimensional shallow water equations and simulating the Mosul dam break. The computational domain discretized using unstructured triangular mesh. The solver applied Harten lax van leer with contact (HLLC) wave approximate Riemann solver to calculate the cell interface fluxes, and the semi-implicit scheme employed to solve the friction source term. The numerical scheme applied to two benchmark test cases, and the results showed that the presented model was robust and accurate especially in handling wet/dry beds, mixed flow regimes, discontinuities, negative water depths, and complex topography. The results of this study demonstrate that flood waves may reach the center of Mosul city in < 6 h and water depth may rise to 34 m after 7 h of Mosul dam breaking. Finally, the simulation results of the Mosul dam break were used to prepare an emergency action plan.

The [formula omitted]-ALE-SPH model: An arbitrary Lagrangian-Eulerian framework for the [formula omitted]-SPH model with particle shifting technique

The behaviour of a weakly-compressible SPH scheme obtained by rewriting the Navier-Stokes equations in an arbitrary Lagrangian-Eulerian (ALE) format is studied. Differently from previous works on ALE, which generally adopt conservative variables (i.e. mass and momentum) and rely on the use of Riemann solvers inside the spatial operators, the proposed model is expressed in terms of primitive variables (i.e. density and velocity) and is written by using the standard differential formulations of the weakly-compressible SPH schemes. Similarly to ALE-SPH models, the arbitrary velocity field is obtained by modifying the pure Lagrangian velocity of the material point through a velocity δu→ given by a Particle Shifting Technique (PST). We show that the above-mentioned ALE-SPH equations are, however, unstable when they are integrated in time. The instability appears in the form of large volume variations in those fluid regions characterised by high velocity strain rates. Nonetheless, the scheme can be stabilised if appropriate diffusion terms are included in both the equations of density and mass. This latter scheme, hereinafter called δ-ALE-SPH scheme, is validated against reference benchmark test-cases: the viscous flow around an inclined elliptical cylinder, the lid-driven cavity and a dam-break flow impacting a vertical wall.

Constrained multi-fidelity surrogate framework using Bayesian optimization with non-intrusive reduced-order basis

This article addresses the problem of constrained derivative-free optimization in a multi-fidelity (or variable-complexity) framework using Bayesian optimization techniques. It is assumed that the objective and constraints involved in the optimization problem can be evaluated using either an accurate but time-consuming computer program or a fast lower-fidelity one. In this setting, the aim is to solve the optimization problem using as few calls to the high-fidelity program as possible. To this end, it is proposed to use Gaussian process models with trend functions built from the projection of low-fidelity solutions on a reduced-order basis synthesized from scarce high-fidelity snapshots. A study on the ability of such models to accurately represent the objective and the constraints and a comparison of two improvement-based infill strategies are performed on a representative benchmark test case.

Channel segregation during columnar solidification: Relation between mushy zone instability and mush permeability

A model of mushy zone instability is developed for characterization and prediction of channel segregation in castings. The model highlights the connection of the mushy zone instability with the mush permeability. A new criterion for amplification of the mush instability is derived, which depends on the interdendritic velocity, the isotherm velocity, the temperature gradient, and explicitly on the mush permeability. The capability of the instability criterion in the characterization of channel segregates is illustrated by comparing the estimated possible channel locations with that of numerically simulated channel segregations in a benchmark test case of solidification of Sn-Pb alloy. An Opensource CFD software OpenFOAM is used to simulate the solidification of Sn-Pb alloy in a side-cooled rectangular cavity. The new instability criterion very well characterizes the channel segregates shown in the numerical simulations. The near-liquidus part of the mushy region is more prone to the initiation of instability, which can initiate the formation of channel segregates in castings. Permeability and its derivative with respect to the liquid fraction in the outer part of mushy zone (liquid fraction more than 0.9) plays a key role in the amplification of this instability that can be responsible for the development and the formation of channel segregates. The locations of channel segregates estimated by the new instability model are also compared with those with a remelting criterion, and it has been noticed that the remelting criterion severely under characterizes these defects (e.g., their number and length). We noticed that local remelting might not be necessary for the initiation of a channel; some destabilization of the mushy zone due to local instability could be sufficient.

Spatial adaptivity of the SAAF and Weighted Least Squares (WLS) forms of the neutron transport equation using constraint based, locally refined, isogeometric analysis (IGA) with dual weighted residual (DWR) error measures

This paper describes a methodology that enables NURBS (Non-Uniform Rational B-spline) based Isogeometric Analysis (IGA) to be locally refined. The methodology is applied to continuous Bubnov-Galerkin IGA spatial discretisations of second-order forms of the neutron transport equation. In particular this paper focuses on the self-adjoint angular flux (SAAF) and weighted least squares (WLS) equations. Local refinement is achieved by constraining degrees of freedom on interfaces between NURBS patches that have different levels of spatial refinement. In order to effectively utilise constraint based local refinement, adaptive mesh refinement (AMR) algorithms driven by a heuristic error measure or forward error indicator (FEI) and a dual weighted residual (DWR) or goal-based error measure (WEI) are derived. These utilise projection operators between different NURBS meshes to reduce the amount of computational effort required to calculate the error indicators. In order to apply the WEI to the SAAF and WLS second-order forms of the neutron transport equation the adjoint of these equations are required. The physical adjoint formulations are derived and the process of selecting source terms for the adjoint neutron transport equation in order to calculate the error in a given quantity of interest (QoI) is discussed. Several numerical verification benchmark test cases are utilised to investigate how the constraint based local refinement affects the numerical accuracy and the rate of convergence of the NURBS based IGA spatial discretisation. The nuclear reactor physics verification benchmark test cases show that both AMR algorithms are superior to uniform refinement with respect to accuracy per degree of freedom. Furthermore, it is demonstrated that for global QoI the FEI driven AMR and WEI driven AMR produce similar results. However, if local QoI are desired then WEI driven AMR algorithm is more computationally efficient and accurate per degree of freedom.

The Cross-Entropy Method for the Winner Determination Problem in Combinatorial Auctions

The combinatorial auction is one of the important methods used for multi-item auctions, and the solution to the winner determination problem (WDP) is the key factor in the widespread application of combinatorial auctions. This paper explores the use of the cross-entropy method to solve the WDP, which is an NP problem. The performance of the proposed approach is evaluated on the basis of two well-known benchmark test cases. The experimental results show that, compared with the genetic algorithm and the particle swarm optimization algorithm, the cross-entropy（CE）method has the advantages of a higher success rate and a shorter time for solving the WDP. Therefore, the CE method provides a high-quality solution for the effective solution of the problem of determining winning bids in combined auctions.

Effects of interphase momentum exchange models on simulation of subcooled flow boiling

This research aimed to explore the accuracy of different momentum exchange models in the Eulerian multiphase method. Effects of different correlations for interaction forces on predicting of subcooled fluid flow boiling parameters in heated vertical tubes were studied numerically. Specifically, numerical simulations were carried out using several combinations of the momentum exchange coefficients separately. The results were compared with the experimental data of two benchmark test cases, and the error percentages were calculated. Results indicated that the accuracy of the two-phase simulations depended on the selection of the appropriate combination of momentum exchange models. However, it was found that modeling drag with Ishii and Universal, lift with Moraga and Saffman, wall lubrication with Antal et al. and Hosokawa, turbulent dispersion with De Bertodano, and turbulent interaction with Troshko-Hassan correlations generally led to higher accuracy. The results showed that the experimental benchmark data could be simulated numerically with the minimum relative error of 6.97%. The study also showed that wall lubrication and lift had negligible impacts on the numerical results for most working conditions.

Numerical cavitation noise prediction of a benchmark research vessel propeller

This paper presents the preliminary results of a numerical study for noise prediction of a benchmark propeller in open water/uniform flow conditions. The experimental benchmark test data for the research vessel, “The Princess Royal”, were used for validation purposes. The numerical analyses were implemented by using a viscous solver based on the finite volume method while the experimental data were obtained from model tests conducted at the Genova University Cavitation Tunnel. The main aim of the study is to predict propeller hydro-acoustic performance under cavitating conditions. The hydrodynamic flow field was solved using a RANS (Reynolds-averaged Navier-Stokes) solver. The Schnerr-Sauer cavitation model based on a reduced Rayleigh-Plesset equation together with a VOF approach was used to model sheet cavitation on the propeller blades. The computed hydrodynamic characteristics and sheet cavity patterns were shown to be in good agreement with the Genoa experimental data, thus providing a firm basis for cavitating noise predictions. The hydro-acoustic performance of the model propeller was predicted by using a hybrid method. In the noise simulations, RANS equations were equipped with a porous FW-H (Ffowcs Williams-Hawkings) formulation. The different propeller operational conditions were simulated using this hybrid method. The numerical results were also validated with the experimental data for the propeller hydro-acoustic performance. Whereas such validations showed promising results by means of overall noise spectrum with the benchmark test cases in the low-frequency range, the numerical prediction overestimated the 1st BPF values (around 20 dB) in five loading conditions. Besides, in some loading conditions, especially between 200 and 800 Hz, the difference between numerical predictions and the experiment was found around 5–10 dB.