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This paper presents an alternative well-balanced and energy stable method for the system of non-homogeneous Shallow Water Equations (SWE) on unstructured grids based on the residual distribution (RD) approach. The motivation of the work is based on the grid insensitivity of RD method. The newly proposed method has a positive first order part, a linearity-preserving second order scheme as well as a limited scheme which works for both steady and unsteady problems using simple, explicit time integration techniques. Numerical results herein confirm the accuracy and efficacy of the new methods in preserving both energy stability and well-balancedness. [ABSTRACT FROM AUTHOR]

In this work, we prove the convergence of residual distribution (RD) schemes to dissipative weak solutions of the Euler equations. We need to guarantee that the RD schemes are fulfilling the underlying structure preserving methods properties such as positivity of density and internal energy. Consequently, the RD schemes lead to a consistent and stable approximation of the Euler equations. Our result can be seen as a generalization of the Lax–Richtmyer equivalence theorem to nonlinear problems that consistency plus stability is equivalent to convergence. [ABSTRACT FROM AUTHOR]

The Deferred Correction (DeC) methods combined with the residual distribution (RD) approach allow the construction of high order continuous Galerkin (cG) schemes avoiding the inversion of the mass matrix. With the application of entropy correction functions we can even obtain entropy conservative/dissipative spatial discretizations in this context. To handle entropy production in time, a relaxation approach has been suggested by Ketcheson. The main idea is to slightly modify the time-step size such that the approximated solution fulfills the underlying entropy conservation/dissipation constraint. In this paper, we first study the relaxation technique applied to the DeC approach as an ODE solver, then we extend this combination to the residual distribution method, requiring more technical steps. The outcome is a class of cG methods that is fully entropy conservative/dissipative and where we can still avoid the inversion of a mass matrix. [ABSTRACT FROM AUTHOR]

Structural Health Monitoring (SHM) has enabled the condition of large structures, like bridges, to be evaluated in real time. In order to monitor behavioral changes, it is essential to identify parameters of the structure that are sensitive enough to capture damage as it develops while being stable enough during ambient behavior of the structure. Research has shown that monitoring the neutral axis (N.A.) position satisfies the first criterion of sensitivity; however, monitoring N.A. location is challenging because its position is affected by the loads applied to the structure. The motivation behind this research comes from the greater than expected impact of various load characteristics on observed N.A. location. This paper develops an indirect way to estimate the characteristics of vehicular loads (magnitude and lateral position of the load) and uses a data mining approach to predict the expected location of the N.A. Instead of monitoring the behavior of the N.A., in the proposed method the residuals between the monitored and predicted N.A. location are monitored. Using actual SHM data collected from a cable-stayed bridge, over a 2-year period, the paper presents the steps to be followed for creating a data mining model to predict N.A. location, the use of monthly sample residuals of N.A. to capture behavioral changes, the ability of the method to distinguish between changes in the load characteristics from behavioral changes of the structure (e.g. change in response due to cracking, bearings becoming frozen, cables losing tension, etc.), and the high sensitivity of the method that allows capturing of minor changes.

Based on the field survey in Dongxiang Autonomous County of Gansu Province in 2017 and 2018, we found and obtained rich effective Dongxiang folk story resources. These first-hand story resources remain in relatively remote area of the county, with elderly women in the Dongxiang Language Reservation Area in the central and east of the county a the main oral inheritance group. The distribution characteristics of folk stories: few people pressure most stories, while most people could not narrate complete stories, and few traditional story resources are widespread. At present, due to various reasons, the oral environment and inheritance status of folk stories in Dongxiang County is not optimistic, the survey is difficult, and the story resources are scattered, and there is a tendency to gradually disappear. Therefore, it is necessary to actively protect the existing Dongxiang folk: artists and folic story resources, and to conduct digital sorting of these resources in time. [ABSTRACT FROM AUTHOR]

This work introduces an extension of the residual distribution (RD) framework to stiff relaxation problems. The RD is a class of schemes which is used to solve a hyperbolic system of partial differential equations. To our knowledge, it has been used only for systems with mild source terms, such as gravitation problems or shallow water equations. What we propose is an implicit-explicit (IMEX) version of the RD schemes that can resolve stiff source terms, without refining the discretization up to the stiffness scale. This can be particularly useful in various models, where the stiffness is given by topological or physical quantities, e.g., multiphase ows, kinetic models, or viscoelasticity problems. We will focus on kinetic models that are BGK approximation of hyperbolic conservation laws. The extension to more complicated problems will be carried out in future works. The provided scheme is able to catch different relaxation scales automatically, without losing accuracy; we prove that the scheme is asymptotic preserving and this guarantees that, in the relaxation limit, we recast the expected macroscopic behavior. To get a high order accuracy, we use an IMEX time discretization combined with a deferred correction procedure, while naturally RD provides high order space discretization. Finally, we show some numerical tests in one and two dimensions for stiff systems of equations. [ABSTRACT FROM AUTHOR]

High-efficiency video coding (HEVC) utilizes a quadtree-structured coding unit (CU) for more possible sizes of basic blocks for later prediction. The exhaustive search for the optimal CU depth requires high complexity, which causes difficulties for real-time streaming. In the proposed method, we make use of the residual statistics of prediction units (PUs) in the current encoded CU to make a decision on CU early termination. The residual histogram is discussed, and the optimal early termination (ET) zone is designed; if the PU residual statistics fall in the ET zone, the early termination is triggered. The optimal parameters for the ET zone are solved and analyzed in the training stage, and can be estimated with table lookup and simple computations in the testing stage. Another early termination method using the neighboring SKIP information is also proposed. We use SKIP information from more meaningful CU neighbors defined and used in HEVC. We combine the proposed residual-based and SKIP-based algorithms with a state-of-the-art method. The experimental results show that compared to two state-of-the-art methods in both low delay (LP) and random access (RA) configurations, our preferred proposed combination can achieve the best BDBR results (0.737 % in LP and 0.471 % in RA) with a good corresponding TS performances (49.87 % in LP and 54.96 % in RA), making HEVC more suitable for real-time applications. [ABSTRACT FROM AUTHOR]

In the present work, a high order finite element type residual distribution scheme is designed in the framework of multidimensional compressible Euler equations of gas dynamics. The strengths of the proposed approximation rely on the generic spatial discretization of the model equations using a continuous finite element type approximation technique, while avoiding the solution of a large linear system with a sparse mass matrix which would come along with any standard ODE solver in a classical finite element approach to advance the solution in time. In this work, we propose a new Residual Distribution (RD) scheme, which provides an arbitrary explicit high order approximation of the smooth solutions of the Euler equations both in space and time. The design of the scheme via the coupling of the RD formulation (Ricchiuto and Abgrall, 2010; Abgrall, 2006) with a Deferred Correction (DeC) type method (Liu et al., 2008; Minion, 2003), allows to have the matrix associated to the update in time, which needs to be inverted, to be diagonal. The use of Bernstein polynomials as shape functions, guarantees that this diagonal matrix is invertible and ensures strict positivity of the resulting diagonal matrix coefficients. This work is the extension of Abgrall et al. (2016) and Abgrall (2017) to multidimensional systems. We have assessed our method on several challenging benchmark problems for one- and two-dimensional Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions. [ABSTRACT FROM AUTHOR]

An entropy-stable residual distribution (RD) method is developed for the systems of two-dimensional shallow water equations (SWE). The construction of entropy stability for the residual distribution method is derived from finite volume method principles, albeit using a multidimensional approach. The paper delves into in-depth discussions on how finite volume methods achieve entropy stability in a "one-dimensional" sense for two-dimensional systems of SWE unlike the residual distribution methods. Results herein demonstrate the superiority of the entropy-stable RD methods relative to their finite volume counterparts, especially on highly irregular triangular grids. The comparative results with other established RD methods are also included, depicting similar performances with the Lax–Wendroff method for unsteady smooth flows but more accurate than the multidimensional upwind approaches (N, LDA) on both smooth and discontinuous test cases. [ABSTRACT FROM AUTHOR]

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used to compute the numerical fluxes and source term based on the point values of the solution, and the principles of residual distribution schemes are adapted to obtain steady state solutions. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency, high order accuracy and the capability of resolving shocks of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract In this work, we present a model order reduction (MOR) technique for hyperbolic conservation laws with applications in uncertainty quantification (UQ). The problem consists of a parametrized time dependent hyperbolic system of equations, where the parameters affect the initial conditions and the fluxes in a non- linear way. The procedure utilized to reduce the order is a combination of a Greedy algorithm in the parameter space, a proper orthogonal decomposition (POD) in time and empirical interpolation method (EIM) to deal with non-linearities (Drohmann, 2012). We provide under some hypothesis an error bound for the reduced solution with respect to the high order one. The algorithm shows small errors and savings of the computational time up to 90% in the UQ simulations, which are performed to validate the algorithm. [ABSTRACT FROM AUTHOR]

Summary: Although all of the main properties of a ground motion cannot be captured through a single parameter, a number of different engineering parameters has been proposed that are able to reflect either one or more ground‐motion characteristics concurrently. For many of these parameters, especially regarding Greece, there are relatively few or no predictive models. In this context, we present a set of new regionally‐calibrated equations for the prediction of the geometric mean of the horizontal components of 10 amplitude‐, frequency response‐, and duration‐based parameters for shallow crustal earthquakes. These equations supersede previous empirical relationships for Greece since their applicability range for magnitude, and epicentral distance has been extended down to Mw 4 and up to 200 km, respectively, the incorporation of a term accounting for anelastic attenuation has been investigated, while their development was based on a ground‐motion dataset spanning from 1973 to 2014. For all ground‐motion parameters, we provide alternative optimal equations relative to the availability of information on the different explanatory variables. In all velocity‐based and contrary to the acceleration‐based parameters, the anelastic attenuation coefficient was found statistically insignificant when it was combined with the geometric decay and the coefficient accounting for saturation with distance. In the regressions where the geometric decay coefficient simultaneously incorporated the contribution of anelastic attenuation, its increase was found to be much less considerable in the velocity‐based than in the acceleration‐based parameters, implying a stronger effect of anelastic attenuation on the parameters that are defined via the acceleration time history. [ABSTRACT FROM AUTHOR]

This paper solves the advection-diffusion equation by treating both advection and diffusion residuals in a separate (non-unified) manner. An alternative residual distribution (RD) method combined with the Galerkin method is proposed to solve the advection-diffusion problem. This Flux-Difference RD method maintains a compact-stencil and the whole process of solving advection-diffusion does not require additional equations to be solved. A general mathematical analysis reveals that the new RD method is linearity preserving on arbitrary grids for the steady-state advection-diffusion equation. The numerical results show that the flux difference RD method preserves second-order accuracy on various unstructured grids including highly randomized anisotropic grids on both the linear and nonlinear scalar advection-diffusion cases. [ABSTRACT FROM AUTHOR]

In this paper, the properties of the newly developed flux-difference residual distribution methods will be analyzed. The focus would be on the order-of-accuracy and stability variations with respect to changes in grid skewness. Overall, the accuracy loss and the stability range of the new methods are comparable with the existing residual distribution methods. It will also be shown that new method has a general mathematical formulation which can easily recover the existing residual distribution methods. [ABSTRACT FROM AUTHOR]

An efficient method has been developed for determining tridemorph in banana using high-performance liquid chromatography–tandem mass spectrometry (HPLC-MS/MS). The dissipation and terminal residue of tridemorph in banana fields were carried out at good agricultural practice (GAP) conditions. The average recoveries ranged from 84.4% to 90.0% with relative standard deviations (RSDs) of 3.0%–7.0% at three different spiking levels. The results indicated that the tridemorph dissipated quickly in banana with half-lives of 7.0–7.7 days. The results of residual distribution ranged from 0.01 to 0.26 mg/kg, 0.01–0.62 mg/kg and <0.01 mg/kg in whole banana, peel and pulp, respectively. The relationship between application factor and residue was discussed. The results of risk assessment showed that the risk quotient ( RQ ) value was all below RQ = 1. Given that China has not set an maximum residue limit (MRL) value for tridemorph in banana, this study could provide guidance for the reasonable use of tridemorph. [ABSTRACT FROM AUTHOR]

We consider the numerical solution of steady radiative transfer equations on unstructured meshes. The radiative transfer equations belong to a class of integro-differential equations. We apply conservative residual distribution (RD) methods to solve the radiative transfer equations. To achieve this, we first adopt the discrete ordinate method for angular discretization and use the RD methods to solve the resulting system of coupled linear hyperbolic equations. We present some basics and accuracy analysis for the RD schemes. The standard nonlinear limiter is adopted to upgrade the monotonicity preserving first-order scheme for a high-order one. Several numerical experiments show that the proposed RD schemes achieve second-order accuracy and verify the non-oscillatory property of our numerical schemes. [ABSTRACT FROM AUTHOR]

This paper presents an analytical and numerical approach in studying accuracy deterioration of residual distribution and cell-vertex finite volume methods on triangular grids. Results herein demonstrate that both methods preserve the order-of-accuracy reasonably well for uniformly skewed triangular grids and the $$L_2$$ errors of both second-order accurate methods behave similarly with values of the same magnitude. On the other hand, the first-order finite volume method has an $$L_2$$ error of about an order of magnitude higher than its residual distribution counterpart. Both first-order methods are unable to preserve the order-of-accuracy for high-frequency data when the grids are highly skewed although the residual distribution approach has a slightly better performance. Both second-order methods perform quite decently for high-frequency data on uniformly skewed grids. However, the order-of-accuracy of finite volume methods excessively deteriorate when the grids are skewed non-uniformly unlike the residual distribution methods which preserve the order-of-accuracy. [ABSTRACT FROM AUTHOR]

The performance of the classic upwind-type residual distribution (RD) methods on skewed triangular grids are rigorously investigated in this paper. Based on an improved signals distribution, an improved second order RD method based on the LDA approach is proposed to faithfully replicate the flow physics on skewed triangular grids. It will be mathematically and numerically shown that the improved LDA method is found to have minimal accuracy variations when grids are skewed compared to classic RD and cell vertex finite volume methods on scalar equations and system of Euler equations. [ABSTRACT FROM AUTHOR]

Three-phase displacement events often occur in unsaturated porous media, especially when immiscible contaminants (e.g., non-aqueous phase liquid, NAPL) inadvertently enter the subsurface. In this study, the influence of initial water saturation on the three-phase displacement efficiency and residual distribution during NAPL invasion into unsaturated porous media was experimentally investigated. The low-field nuclear magnetic resonance (LF-NMR) technique was used to dynamically monitor the spatial distribution of water in unsaturated porous media during the invasion of NAPL. The residual distributions (e.g., volume fraction) of NAPL/water/gas were quantitatively analyzed. The results showed that both the initial water saturation and the NAPL injection rate had a significant influence on the three-phase displacement. We found that the displacement efficiency of water/gas exhibited a non-monotonic relationship with the initial water saturation in the unsaturated porous media at certain NAPL invasion rates. A method was proposed to characterize the three-phase displacement regime in terms of the classical two-phase Lenormand's diagram. A significant increase in the volume fraction of residual NAPL after NAPL invasion was observed during the transition from the strong drainage region to the transitional displacement region. However, the initial water saturation was insensitive to the volume fraction of residual NAPL, once the characterized three-phase displacement regime transitioned to the stable displacement region. This study not only highlighted the influence mechanism of initial water saturation and NAPL injection rate on the three-phase displacement efficiency, but also endowed the classical two-phase Lenormand's diagram with the three-phase displacement regime. [ABSTRACT FROM AUTHOR]

This paper presents preliminary developments of entropy-stable residual distribution methods for scalar problems. Controlling entropy generation is achieved by formulating an entropy conserved signals distribution coupled with an entropy-stable signals distribution. Numerical results of the entropy-stable residual distribution methods are accurate and comparable with the classic residual distribution methods for steady-state problems. High order accurate extensions for the new method on steady-state problems are also demonstrated. Moreover, the new method preserves second order accuracy on unsteady problems using an explicit time integration scheme. The idea of the multi-dimensional entropy-stable residual distribution method is generic enough to be extended to the system of hyperbolic equations, which will be presented in the sequel of this paper. [ABSTRACT FROM AUTHOR]

The presence of faults in industrial processes represents a serious threat, which can lead to performance degradation as well as damage to human health. The early detection of change might avoid undesired consequences. This study proposes a fault detection (FD) method based on the probability distribution measure. The method needs the generation of residual. To this end, the residual is obtained from applying a non‐linear auto‐regressive moving average with exogenous input model. To detect a fault, this approach compares the probability density of current residual against a reference one, using the Hellinger distance (HD). The change detection problem is formulated in terms of distance measures that characterise the similarity of distributions of the residual. Sensitivity analysis on the HD under normal distribution assumption is performed. To demonstrate the satisfying performance of the proposed FD technique, a distillation plant at the laboratory scale is used as the case study. [ABSTRACT FROM AUTHOR]

A high-order Residual Distribution scheme for the solution of the compressible RANS equations is developed. The one-equation Spalart–Allmaras turbulence model is solved together with the RANS equations as a fully coupled system, in which both the mean flow equations and the turbulence equation are solved with high-order of accuracy. A continuous approximation of the solution is adopted and standard Lagrangian basis functions are used to construct the discrete space. Since viscous terms involve the gradient of the numerical solution which has a discontinuous normal component across the faces of the elements, a continuous approximation of the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same basis functions used for the solution. The non-linear system of equations resulting from the numerical discretization is solved with the non-linear LU-SGS method. Several numerical experiments are performed to verify the accuracy of the numerical method, these are based on both subsonic and transonic flows in two and three spatial dimensions. [ABSTRACT FROM AUTHOR]