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In this paper, we consider an inverse problem related to a fractional diffusion equation. The model problem is governed by a nonlinear partial differential equation involving the fractional spectral Laplacian. This study is focused on the reconstruction of an unknown source term from a partial internal measured data. The considered ill‐posed inverse problem is formulated as a minimization one. The existence, uniqueness, and stability of the solution are discussed. Some theoretical results are established. The numerical reconstruction of the unknown source term is investigated using an iterative process. The proposed method involves a denoising procedure at each iteration step and provides a sequence of source term approximations converging in norm to the actual solution of the minimization problem. Some numerical results are presented to show the efficiency and the accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

This study presents a three-level explicit time-split MacCormack method to compute approximate solutions of two-dimensional time-dependent linear convection-diffusion-reaction equations with source term. The difference operators split the two-dimensional problem into two pieces so that each subproblem is easily solvable using the original MacCormack approach. Second order accuracy in time and fourth-order convergence in space are achieved by the application of the Taylor series expansion. The proposed algorithm minimizes the computational time, computer memory requirement and is easy to implement. Under a suitable time-step restriction, both stability and error estimates of the numerical scheme are deeply analysed in L ∞ (0 , T ; L 2) -norm. Numerical evidences which confirm the theoretical analysis are considered and discussed. [ABSTRACT FROM AUTHOR]

A new method for the numerical solution of the passive scalar transport equation in the framework of hydrodynamic equations in the shallow water approximation is described. The method is based on previously developed quasi-gasdynamic algorithms for numerical simulation of compressible gas flows. Smoothed equations are derived, and their difference approximations, including for flows with a pollutant source, are presented. The numerical algorithms are tested as applied to one- and two-dimensional flows. As an example, the algorithm is used to solve the problem of water circulation in Lake Vallunden. The constructed approach is generalized to passive scalar transport in the case of viscous incompressible flows. [ABSTRACT FROM AUTHOR]

This work studies the blow-up result of the solution of a coupled nonlocal singular viscoelastic equation with general source and localized frictional damping terms under some suitable conditions. This work is a natural continuation of the previous recent articles by Boulaaras et al. (Appl. Anal., 2020, 10.1080/00036811.2020.1760250; Math. Methods Appl. Sci. 43:6140–6164, 2020; Topol. Methods Nonlinear Anal., 2020, 10.12775/TMNA.2020.014). [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear wave equation with damping and source terms of variable-exponent types. First, we use the stable-set method to prove a global result. Then, by applying an integral inequality due to Komornik, we obtain the stability result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the decay property of a nonlinear viscoelastic wave equation with linear damping, nonlinear damping and source term. Under weaker assumption on the relaxation function, we establish a general decay result, which extends the result obtained in Messaoudi [Exponential decay of solutions of a nonlinearly damped wave equation. Nodea-Nonlinear Differ Equat Appl. 2005;12:391–399]. [ABSTRACT FROM AUTHOR]

In this paper, we develop numerical methods based on the fuzzy transform methods (FTMs). In this approach we apply fuzzy transforms on discrete version of the derivatives and use it to derive FTMs. We also establish convergence of the proposed FTMs. To test the efficiency of the proposed FTMs, we apply the FTM schemes on the second order nonlinear singular boundary value problems and fourth order BVPs. We allow the source term of the differential equation to have jump discontinuity and study the effect of jump on FTMs and finite difference methods. The work shows that FTMs are better for both class of BVPs considered in this paper, having singularity, nonlinearity and jump discontinuity. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inverse problem of identifying the source term for a generalization of the time-fractional diffusion equation, where regularized hyper-Bessel operator is used instead of the time derivative. First, we investigate the existence of our source term; the conditional stability for the inverse source problem is also investigated. Then, we show that the backward problem is ill-posed; the fractional Landweber method and the fractional Tikhonov method are used to deal with this inverse problem, and the regularized solution is also obtained. We present convergence rates for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. Finally, we present a numerical example to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider an elastic beam equation with delay, source term, and boundary conditions together with some suitable initial data. Using the Faedo‐Galerkin approximation and some estimates, we get the local existence of solution. Moreover, we obtain the finite time blow‐up of solution by constructing suitable Lyapunov functionals. [ABSTRACT FROM AUTHOR]

The asymptotic behaviors of Riemann solutions for generalized Chaplygin gas magnetohydrodynamic Euler equations with source terms were considered. The self-similarity of the solutions is no longer true due to the inhomogeneous term. They will converge to Riemann solutions for zero-pressure flow transport equations when pressure and magnetic induction disappear at the same time, and δ-shock wave and vacuum will appear in the solutions. The solutions will converge to Riemann solutions for generalized Chaplygin gas Euler equations with inhomogeneous terms in the case of vanishment of magnetic induction, additionally only δ-shock wave appears in the solutions. [ABSTRACT FROM AUTHOR]

In this paper, a generalized lattice Boltzmann (LB) model with a source term in the continuity equation is proposed to solve both incompressible and nearly incompressible Navier–Stokes (N–S) equations. This model can be used to deal with single-phase and two-phase flows problems with a source term in the continuity equation. From this generalized model, we can not only get some existing models, but also derive new models. Moreover, for the incompressible model derived, a modified pressure scheme is introduced to calculate the pressure, and then to ensure the accuracy of the model. In this work, we will focus on a two-phase flow system, and in the frame work of our generalized LB model, a new phase-field-based LB model is developed for incompressible and quasi-incompressible two-phase flows. A series of numerical simulations of some classic physical problems, including a spinodal decomposition, a static droplet, a layered Poiseuille flow, and a bubble rising flow under buoyancy, are performed to validate the developed model. Besides, some comparisons with previous quasi-incompressible and incompressible LB models are also carried out, and the results show that the present model is accurate in the study of two-phase flows. Finally, we also conduct a comparison between quasi-incompressible and incompressible LB models for two-phase flow problems, and find that in some cases, the proposed quasi-incompressible LB model performs better than incompressible LB models. [ABSTRACT FROM AUTHOR]

• A scenario of SGTR + SLB was simulated in a three-loop Western 1000 MWe PWR. • A comparison is carried out between MELCOR 2.2 and CATHARE 2 codes. • The analysis is focused on thermal–hydraulic and FP releases. • The results are compared, discussed and the differences highlighted. The European project denominated Reduction of Radiological Consequences of design basis and design extension Accidents (R2CA) was launched in September 2019, with a very broad participation: 11 countries, 17 participating organisations, including international organisations, utilities, regulators, technical support organisations, researchers and developers and was coordinated by IRSN. The main goal of the project was to assess the conservatisms in the radiological releases calculations in nuclear power plant (NPP) studies. The work here presented is focused on developing new calculation methodologies and updating computer code models to carry out more detailed assessments of source terms resulting from a steam generator tube rupture (SGTR) accident in the Design Extension conditions A (DEC-A) domain. For this purpose, participants in Work Package 2 (WP2) of R2CA developed and implemented simplified models in the Severe Accident (SA) and Thermal-Hydraulic (TH) codes that take into account iodine spiking and iodine transport phenomena within primary and secondary circuit. These methodologies will not only provide a better estimation of the radiological consequences, but should also serve to improve accident management procedures, innovative instrumentation development and early detection tools. The new approaches are tested in a SGTR + Steam Line Break Outside Containment scenario without significant fuel degradation in a three-loop Western 1000 MW e PWR. During the transient, operators are also assumed to implement emergency operating procedures (EOPs) in line with Westinghouse EOPs to limit the release of radioactivity and control the evolution of plant parameters. The calculations are performed by Tractebel and CIEMAT with the American SA tool MELCOR and Bel-V with the French TH code CATHARE. The results highlighted some limitations of implemented models in predicting iodine behaviour as well as small discrepancies in the TH evolution of the transient, both of which were analysed and discussed in detail. [ABSTRACT FROM AUTHOR]

• Indication of interaction between tellurium aerosols and organic species was studied. • In the presence of organic gases, increase of tellurium concentration in the liquid trap was observed. • XPS analysis shows changes in tellurium speciation and oxidation state in the presence of organic material. • The potential formation of volatile tellurium species raises safety concerns in severe accident scenarios. One of the volatile fission products potentially released during a severe nuclear accident is tellurium. Recently, tellurium has been shown to form volatile organic tellurides from paint solvents in aqueous solutions which could further increase the release. However, not much is known about the possible interactions between tellurium and organic material in gas phase. In this study, tellurium was exposed to conditions simulating the containment atmosphere during an accident. Moreover, volatile organic compounds were introduced to the gas phase representing the presence of organic material in the containment during the accident. The results suggest that tellurium aerosols and organic material interact in the gas phase which was observed as an increase in the gaseous fraction and a change in the XPS spectra. Although no exact species were identified, the results raise questions about the behavior of tellurium in severe accident conditions, especially, regarding the reactions involving organic material. [ABSTRACT FROM AUTHOR]

For the analysis of the aerodynamic characteristics of the buildings immersed in the atmospheric boundary layer (ABL), it is necessary to generate a turbulence velocity field with similar temporal and special characteristics to the ABL to obtain a reliable result. In this paper, an improved precursor simulation method called the recycling and reshaping method (RRM) is proposed to generate a turbulent boundary layer in an LES model. The laminar inflow is firstly disturbed by the virtual roughness blocks realized by adding drag force term in the momentum equation, then the inflow velocity profile is reshaped every several steps to adjust the streamwise velocity profile in the downstream target area to meet the requirements. The final turbulence field generated by RRM with virtual roughness blocks is in good agreement with the target velocity conditions. Then, the simulation of the wind-induced pressure on an isolated low-rise building surface is carried out, using the generated turbulence boundary layer as inflow. The comparison between numerical results and TPU aerodynamic database shows that the time-averaged wind-induced surface pressure obtained by LES can be considered in good accordance with the measurements over the whole building surface. However, the non-ignorable deviations for the fluctuating pressure result in the flow separation corners still exist.

In this work, we investigate the inverse problem of identifying a space-wise dependent source term of wave equation from the measurement on the boundary. On the basis of the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are obtained. The projected gradient method and two-parameter model function method are applied to the minimization problem and numerical results are illustrated.

The purpose of this article is to study the asymptotic analysis of the solutions of a linear viscoelastic problem with a dissipative and source terms in a three‐dimensional thin domain Ωε. Firstly, we give the strong formulation of the problem and the existence and uniqueness theorem of the weak solution. Then, we establish some estimates independent of the parameter ε. These last will be useful to obtain the limit problem with a specific weak form of the Reynolds equation. [ABSTRACT FROM AUTHOR]

• We calculate the accumulation of ruthenium with SCALE code and analyze the distribution of ruthenium-106 under different injection temperatures with ASTEC code. • In deposited aerosol phase, the RuO and RuO 2 increase with temperature, however the RuO 3 increases rapidly and reaches equilibrium at a certain temperature. • In suspended phase, the accumulation of RuO 3 reaches the maximum at 750 °C. • In gaseous phase, RuO 4 appears when the temperature above 750 °C and RuO 4 mass at 900 °C are three times more than that of at 750 °C. We calculate the accumulation of ruthenium-106 with SCALE code and analyze the distribution of ruthenium-106 under different injection temperatures with ASTEC code. In deposited aerosol phase, the RuO and RuO 2 increase with temperature, however the RuO 3 increases rapidly and reaches equilibrium at a certain temperature of injection source. In suspended aerosol phase, the accumulation of RuO and RuO 2 decreases continuously with rising of temperature, while RuO 3 reaches the maximum at 750 °C. In gaseous phase, the masses of RuO and RuO 2 increase and reach equilibrium rapidly. Similar to gaseous aerosol phase, the accumulation of RuO 3 reaches to the maximum value at 750 °C. RuO 4 appears when the temperature above 750 °C and the RuO 4 mass at 900 °C are three times more than that of at 750 °C. Our results denote that a reasonable control of thermal-hydraulics parameters and redox conditions can effectively constrain the radionuclide ruthenium migration. [ABSTRACT FROM AUTHOR]

A series of experimental tests were performed to measure the efficiency of volatile iodine trapping on sand bed filters and metallic filters. These filtering media are used in French nuclear power plants to mitigate releases in case of severe accident. The results show that molecular iodine is more easily trapped than methyl iodide due to its high chemical affinity with stainless steel or with silver and cesium cations included in the filter medium. For methyl iodide, the trapping efficiency is low. [ABSTRACT FROM AUTHOR]

Fusion reactors represent a future evolution of the nuclear technology improving the world-wide energy portfolio. The experimental fusion reactor under construction (ITER) and the planned industrial fusion reactors (DEMO) are large and complex facilities. For their operation it is necessary to ensure safety limiting of radiological and mobilizable source terms inventory, such as tritium and radioactive dust. The source term inventories shall be assumed in the establishment of operational and safety requirements for DEMO, as well as performing safety analyses for commercial fusion devices. In the last few years a methodology for evaluation of tritium and dust source term inventory has been proposed in the framework of the EUROFusion project. The basis of the methodology is a semi-empirical approach to scale the radioactive inventory limits implemented in ITER. The source term amounts derived for DEMO will supply a guidance for safe operation of future fusion reactors. The development of methodology has to be completed and refined because of the lack of validation versus adequate experimental data and rules for extension to different scenarios. The aim of this work is assessment of the developed methodology for evaluation of the source terms inventory versus JET operating limits for tritium and versus the dust control strategy adopted in ITER for the dust. The updating of the methodology for the dust and T inventory was carried out in line with the current DEMO design. The new values of the in-VV source terms were achieved. These values are recommended to be used for the safety assessment of the fusion reactor. Calculated DST and TST inventories' values show a reasonable agreement with scaled ITER or assessed JET limits. [ABSTRACT FROM AUTHOR]

Highlights • A numerical method is developed for iodine-129 release from fuel to coolant. • The diffusion in fuel and mass balances in gap and in coolant are used. • For iodine spiking have also been modeled for given release rates. • Effect of diffusion constant, purification rate and gas escape rate were studied. Abstract A numerical methodology is developed to compute volatile fission fragment release from fuel to gap and then to the primary coolant under changing reactor conditions. Based on diffusion of fission fragments and mass balances in gap and in coolant, a FORTRAN-77 based program DIFFP (Diffusion of Fission Products) has been developed to solve numerically the time & space dependent equations using source release rate respectively. For power shutdown effect of spiking have been modeled for given release rate. The predicted gas fractional release as a function of time using DIFFP program was in good agreement with the reported results. Then parametric studies for empirical diffusion constant (D′), coolant purification rate (β P), and gas escape rate coefficient (ν) respectively were done to find the sensitivity of parameters. For operation time >150 days, the sensitivity increases from 4.5% to 20.4% with an increase D′ from 4.1 × 10−10 s−1 to 6.9 × 10−10 s−1 respectively and sensitivity is a nonlinear function of D′ : sensitivity = (- 62.20 ± 0.78) + (16.83 ± 0.37) D ′ D o ′ + (- 0.703 ± 0.0398) D ′ D o ′ 2 where, 0.69 < D ′ / D 0 ′ < 1.17 and D ′ is the reference value (5.9 × 10−10 s−1) for the defective fuel rods. Sensitivity for gas escape rate coefficient (ν) was also determined by increasing it from 5% to 50% from its reference value (1.4 × 10−4 s−1) and results show that the coolants activity becomes insensitive to changes in the gas escape rate coefficient and sensitivity value becomes less than 1% when effective full power days are larger than 150. If coolant purification rate constant (β P) is parametrically changed from 5% to 30%, then the absolute sensitivity value increases from 4.8% to 23% respectively and for all cases, the absolute sensitivity remains independent of time (in terms of effective full power days) for a given value of β P and rises linearly with an increase in the value. [ABSTRACT FROM AUTHOR]

• Computational fluid dynamics was applied to CO 2 adsorption and its auxiliary steps. • The source term model of TSA simulation process was summarized. • The developed model is proofed successfully via verification from existing experimental results. • The length–diameter ratio of reactor was studied for optimization of TSA performance. Numerical study on CO 2 adsorption process could benefit an in-depth understanding on the mechanism of physical phenomena and corresponding engineering design for industrial development of carbon capture. The reactor geometry is critical to the energy-efficient design of CO 2 adsorption capture, considering reactor is the most energy-intensive component in the whole system. Using delicate-designed source term in numerical model, the optimized geometry parameters of reactor could be obtained with an accepted calculation cost. In this paper, the design method on the source terms involved in the simulation process is screened firstly, and the numerical calculation is conducted with case study on Mg-MOF-74. The model took into account the constraints of surface area, the inlet flowrate and the adsorbent quality of reactors. Especially, under the constant surface area, three cases with different combinations of length and diameter are studied, respectively. Furthermore, three cases are revisited and compared under the conditions of the same and different cycle time for a fair performance assessment. The case with a length–diameter ratio of 11.2 performs the best adsorption effect which demonstrated that the optimal geometry parameters of TSA capture could be defined through proposed modeling method and related source terms in this study. [ABSTRACT FROM AUTHOR]

The Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term are studied. The Riemann solutions exactly include two kinds: delta-shock solutions and vacuum solutions. In order to see more clearly the influence of the source term on Riemann solutions, the generalized Rankine-Hugoniot relations of delta shock waves are derived in detail, and the position, propagation speed and strength of delta shock wave are given. It is also shown that, as the source term vanishes, the Riemann solutions converge to the corresponding ones of the homogeneous system, which is just the generalized zero-pressure flow model and contains the one-dimensional zero-pressure flow as a prototypical example. Furthermore, the generalized balance relations associated with the generalized mass and momentum transportation are established for the delta-shock solution. Finally, two typical examples are presented to illustrate the application of our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variable‐coefficient wave equation with nonlinear acoustic boundary conditions and source term. Using the Riemannian geometry method, we prove the general energy decay of the system corresponds to the ordinary differential equation (ODE), which certainly is stable under some suitable assumptions. [ABSTRACT FROM AUTHOR]

The Basic Plan for High-Level Radioactive Waste Management (national WM plan) was established and promulgated, taking into consideration national and international trends on policy and technology development. In order to evaluate the safety for a facility in accordance with the national WM plan, it is essential to evaluate the spent nuclear fuel (SNF) source term. The objective of this study was to analyze Korea SNF characteristics; to propose reference SNF; and to evaluate generation amounts, radioactivity, thermal power, and isotopic composition of SNF in compliance with the national WM plan in order to provide basic information for safety research in Korea. The Automatic Multi-batch ORIGEN Runner for Evaluation of Spent fuel program (AMORES) was developed and used to evaluate inventory, radioactivity, and thermal power. Generation amounts, radioactivity, thermal power, and isotopic composition of SNF for milestones in the national WM plan were evaluated using a pressurized water reactor SNF database (DB) through 2015, and future SNF generation was estimated by taking into consideration the distribution of initial enrichment and burnup for each power plant unit. As a result, radioactivity, thermal power, and isotopic composition at each site in 2015, 2052, and 2082 differed significantly depending on the presence of new nuclear power plants. In addition, a reference SNF was proposed through statistical analysis of the SNF DB in order to utilize it for safety analysis based on various scenarios when actual SNF data cannot be available. In order to perform a more realistic safety assessment, radionuclide inventories using reference SNF and time-integrated SNF nuclide inventories using actual data were compared, and then, the best-fit reference SNF for each site and year was suggested. [ABSTRACT FROM AUTHOR]

Abstract We study an Eulerian droplet model which can be seen as the pressureless gas system with a source term, a subsystem of this model and the inviscid Burgers equation with source term. The condition for loss of regularity of a solution to Burgers equation with source term is established. The same condition applies to the Eulerian droplet model and its subsystem. The Riemann problem for the Eulerian droplet model is constructively solved by going through the solution of the Riemann problems for the inviscid Burgers equation with a source term and the subsystem, respectively. Under suitable generalized Rankine–Hugoniot relations and entropy condition, the existence of delta-shock solution is established. The existence of a solution to the generalized Rankine–Hugoniot conditions is proven. Some numerical illustrations are presented. [ABSTRACT FROM AUTHOR]

Highlights • Seismic-generated unsteady motions are modelled by the 2D depth-averaged shallow water equations. • The earthquake-induced forcing effect is represented by a sinusoidal time-dependent source term. • The governing equations are written in nondimensional form to highlight the influential dimensionless parameters. • Exact solutions of smooth waves in a prismatic tank and a rectangular open channel, and of sloshing in a parabolic basin are presented. • The analytical solutions provide a valuable test for the verification of numerical models. Abstract In this paper time-dependent water motions generated by seismic-type horizontal excitation in shallow basins and channels are modelled by the two-dimensional depth-averaged shallow water equations in which a specific source term is added in order to include an earthquake-induced forcing effect. Sinusoidal excitation is considered as a first approximation, and the response of shallow basins and channels to this simple external forcing is characterized. The nondimensional form of the governing equations shows that the Strouhal number and a ratio representing the amplitude of the forcing acceleration are the influential dimensionless parameters. Novel exact solutions of sinusoidally-forced smooth waves in a prismatic tank, a rectangular open channel, and a parabolic basin are presented. In the first two cases, a sway motion occurs, and reflections take place at the side walls. In the last case, the water sloshes back and forth flowing up the sloping sides of the basin; the free surface remains planar and a moving circular shoreline is present. These analytical solutions provide useful standards for assessing the accuracy of the numerical models used to solve the two-dimensional shallow water equations with source terms. [ABSTRACT FROM AUTHOR]

Rapid and accurate prediction and evaluation of accident consequences can provide scientific basis for decision-making of nuclear emergency measures. Accident source term estimation under reactor accident conditions is an important part of nuclear accident consequence evaluation. In order to accurately estimate the information of radioactive source terms released from nuclear power plants to the environment, an inversion model of accident source terms based on BP neural network algorithm (BPNN) was constructed. And to resolve the defect that BPNN is easy to fall into local minimum during training process, genetic algorithm (GA) was used to optimize the weights and thresholds of BPNN. In this paper, referring to the release rates of radioactive source term from the Fukushima nuclear accident. The release rates of 131I and 137Cs diffused into the environment in stable atmosphere were taken as the two target outputs of the GA-BPNN, and the meteorological data for one hour at fixed monitoring points were taken as the target inputs. And the simulation results showed that for the release rate of 131I and 137Cs, the mean relative errors of the training and the testing sample sets were both below 2% which indicates that the GA-BPNN model not only improves the shortcoming of BPNN, but also increases the speed and accuracy of source term inversion. [ABSTRACT FROM AUTHOR]

Extensions to the Roe and HLL method have been previously formulated in order to solve the Shallow Water equations in the presence of source terms. These were named the Augmented Roe (ARoe) method and the HLLS method, respectively. This paper continues developing these formulations by examining how entropy corrections can be appropriately fitted in for the ARoe method and how the HLLS method can be formulated more generally. This is done in two ways. Firstly, this paper extends the reasoning of Harten and Hyman required by the ARoe method to include the source term contributions and thus arrives to a more complete formulation of the entropy fix, which will be compared with the approximation presented in previous works through numerical experiments. Secondly, it is shown how a relaxation of the criteria used when choosing waves in the HLLS method yields better solutions to problems where the HLLS would previously fail. In summary, this paper seeks to offer a comprehensible review of the ARoe and HLLS methods while improving its performance in cases with transcritical rarefactions for the inhomogeneous Shallow Water Equations in one dimension. [ABSTRACT FROM AUTHOR]