## What is/are Integrated Numerical?

Integrated Numerical - The full linear stability equations can also be integrated numerically to directly obtain a complete disturbance profile accounting for the effects of viscosity.^{[1]}To address this issue, we herein introduce an integrated numerical-experimental approach to reconstruct the graft–host response and interrogate the mechanoregulation in dialysis grafts.

^{[2]}The resulting system is integrated numerically utilizing bvp4c tool via MATLAB software.

^{[3]}Vector differential equations are constructed and then integrated numerically over an interval extended from a convenient starting value of the unknown to a value which gives the solution of the system of equations.

^{[4]}Consequently, it becomes necessary to take into account the counter-pressure which has so far been neglected and, when this is included, the partial differential equations describing the flow must be integrated numerically.

^{[5]}An additive manufacturing (AM) functionally graded tungsten carbide using laser directed energy deposition (L-DED) is developed in an integrated numerically controlled multi-axis machining center with multi-material feeding capability.

^{[6]}The interactions of the thermal boundary layer and momentum boundary layer lead to nonlinear similarity equations which are integrated numerically.

^{[7]}Here, we conduct an integrated numerical and experimental study to investigate the feasibility of resonance ultrasound spectroscopy (RUS) as an alternative NDE method to inspect complex AM lattice structures with a varying number of missing struts.

^{[8]}As a result, the equations can be integrated numerically with a relatively high time step making the model suitable for multiscale simulation of the human heart and allowing one to study the impact of myocardial mechanics on arrhythmias.

^{[9]}The parabolic–hyperbolic form of the constraints is integrated numerically.

^{[10]}The equation of motion is integrated numerically in a complex three-dimensional structure via a pseudospectral scheme which, importantly, accounts for lateral heterogeneities in the mechanical properties of bone.

^{[11]}It is integrated numerically and can give rise to a non-Gaussian dynamics.

^{[12]}The transport equations are simplified into ordinary differential equations and then integrated numerically using Runge-Kutta-Fehlberg with shooting technique.

^{[13]}The resulting equations are integrated numerically and the impact of involved parameters on velocity, temperature and nanoparticle concentration presented graphically.

^{[14]}The governing non-linear dynamical equations are integrated numerically by the Runge-Kutta method.

^{[15]}The structures found when a fully-developed rotating Hagen-Poiseuille flow discharges into a much larger pipe section are summarised in a bifurcation diagram, whose coordinates are the Reynolds number of the jet ( Rej) and the swirl parameter ( L), for which the time-dependent, axisymmetric and incompressible Navier-Stokes equations are integrated numerically.

^{[16]}The first-order nonlinear equation is integrated numerically with a modified LSODA 19,20 program.

^{[17]}Also, the Coupled-mode theory is integrated numerically by the Transfer Matrix method to achieve the final equation of the effect of temperature in FBG.

^{[18]}The equations are integrated numerically using a new unconditionally stable method.

^{[19]}The model equation is integrated numerically for the harmonic initial conditions using the discrete Fourier transform-based pseudospectral method.

^{[20]}The analytical model is integrated numerically via an ad hoc algorithm and its reliability & accuracy are verified after various self-consistency tests and comparisons with the literature.

^{[21]}The equations of motion are deduced and integrated numerically.

^{[22]}The basic idea of the approach is to use the analytic expressions of the longitudinal mode fields steady-state solution using Green function) to compute the wakefields at each time step using the macro particle currents as sources, while the Lorentz equations of the particles can be integrated numerically.

^{[23]}The equations for the density contrasts are integrated numerically.

^{[24]}The motion of a prolate particle is developed analytically for asymptotically weak shear thinning and then integrated numerically.

^{[25]}The regular parts of the integrands are integrated numerically.

^{[26]}This study presents an integrated numerical and experimental investigation of a laminated aluminum composite structure.

^{[27]}The equation obtained is integrated numerically.

^{[28]}A penalty method for the revolute joint connecting the slider and other bodies is applied, and equations of motion are integrated numerically.

^{[29]}The velocity data is integrated numerically using an adaptive fourth-order Runge-Kutta method.

^{[30]}To validate the derived equations, the original constitutive model is integrated numerically by applying the time-step procedure for various cyclic loading profiles.

^{[31]}Essentially, a multi-dimensional Fokker-Planck type equation (a parabolic diffusion equation) must be integrated numerically.

^{[32]}The system of equations is integrated numerically in domain [0,∞)by using bvp midrich scheme in Maple software.

^{[33]}As with the predecessor version (TVID 1) the integrals are separated into a known piece, containing the UV divergencies, and a finite piece that is integrated numerically, implemented in C.

^{[34]}Previous modeling work has shown that these phenomena can be described by the same partial differential equation, which must be integrated numerically over two variables, the elapsed time and the donor-acceptor distance.

^{[35]}Moreover, experimental results obtained with the hybrid material, collected under mild regeneration conditions, were used to simulate both CO2 sorption in TGA and packed bed SESMR multicycle tests: a Particle Grain Model (PGM) and an Axial Dispersion Plug Flow Reactor (ADPFR) model were integrated numerically, respectively.

^{[36]}Local volumetric strain caused by soil collapse is estimated using a collapse model and integrated numerically to find the total settlement.

^{[37]}Analytical equations of the drilling system are integrated numerically with finite element method.

^{[38]}It consists of four coupled ordinary differential equations, that were integrated numerically assuming a range of estimates of the key parameters.

^{[39]}Off-shell decays are integrated numerically and a linear interpolation over the resonance is performed.

^{[40]}A lubrication model of the motion is developed, integrated numerically and analysed asymptotically.

^{[41]}

## An Integrated Numerical

An integrated numerical methodology, allowing to couple the full 3D CFD (Computational Fluid Dynamics) flux within the internal chamber of the tyre with an equivalent discrete 3D structure model, is proposed with the aim to completely represent the tyre thermodynamic convective behaviour in the steady-state operating conditions.^{[1]}An integrated numerical procedure that combines LVI with nonlinear Lamb wave detection is developed to predict the nonlinear Lamb wave behavior in LVI-damaged patch-repaired CFRP laminates.

^{[2]}An integrated numerical modelling of discrete element method (DEM) and computational fluid dynamics (CFD) are applied.

^{[3]}An integrated numerical model is established with considering detailed heat transfer and fluid flow in the melting furnace, as well as discrete bubble tracking in molten quartz.

^{[4]}An integrated numerical model was built to predict the quenching and the subsequent cold rolling processes.

^{[5]}An integrated numerical model has been developed based on the General Transport Equation Analysis code.

^{[6]}An integrated numerical method, which couples a seakeeping solver and a Navier-Stokes (NS) solver with the volume of fluid (VOF) model, has been developed to study the behavior of a damage ship in waves.

^{[7]}

## Also Integrated Numerical

The generalized model is also integrated numerically considering two different sets of initial conditions that yield pattern dynamics originating from degradation of uniform vegetation or colonization of bare ground.^{[1]}The hyperbolic model is also integrated numerically to validate the analytical predictions and to characterize more deeply the spatio-temporal evolution of vegetation patterns in both supercritical and subcritical regime.

^{[2]}

## integrated numerical model

In this study, an integrated numerical model was established firstly to recruit both the air chamber and the self-rectifying turbine and associate multiple energy-conversion stages together.^{[1]}According to the monopile-supported wind turbine of Jiangsu Rudong Offshore Wind Farm Demonstration Project, a blade–tower–monopile–soil coupling integrated numerical model considering scour was established in this study, and scour warning indicators and warning limits related to two aspects—dynamic characteristics and dynamic response—were obtained through calculation and analysis.

^{[2]}Overview on Earth System Modelling and Earth System Observations Earth system models (ESMs) combine process-based models of the different sub-systems of the Earth system into an integrated numerical model that yields for a given state of the coupled system at time t the tendencies associated with that state, i.

^{[3]}In this paper, an integrated numerical model is proposed to investigate the effects of particulate size and volume fraction on the deformation, damage, and failure behaviors of particulate-reinforced metal matrix composites (PRMMCs).

^{[4]}Copernicus is organized with a space component, including dedicated Earth Observation satellites (Sentinel missions), and services, which transform the wealth of satellite, in situ and integrated numerical model information into added-value datasets and information usable by scientists, managers and decision-makers, and the wider public.

^{[5]}This paper presents an approach to parametrically simulate the coating thickness in HVOF processes via an integrated numerical model.

^{[6]}Based on the Coupled Eulerian–Lagrangian (CEL) method, an integrated numerical model of sandwich structures is developed to simulate the slamming process, in which the progressive damage evolution of composite material is considered with VUMAT subroutine.

^{[7]}In this study, taking the integrated numerical model FSSI-CAS 2D as the tool, the nonlinear ocean wave & current-induced dynamics of a shallowly buried submarine steel pipeline and its surrounding loosely deposited seabed soil is numerically investigated.

^{[8]}Because the structure included various electrical components, it is hard to establish an accurate and integrated numerical model to simulate the energy delivery and control process.

^{[9]}This study developed an integrated numerical model to simulate disinfection performance of ESD.

^{[10]}In this study, a 2-D integrated numerical model was developed to investigate the stability of the foundation trench under the solitary wave loading.

^{[11]}In this study, a new one-way integrated numerical model for fluid–seabed–structure interaction is established by integrating the finite element software, ABAQUS, and the open-source fluid dynamics package, OlaFlow.

^{[12]}This work presents resent advances on development of integrated numerical models including generation, melting and solidification of the powder bed, considering surface flow, wettability, surface tension and other physical phenomena, specific mechanical and thermo-mechanical aspects and microstructure evolution.

^{[13]}In the present study, an integrated numerical model is developed and applied to investigate the effect of briquette shape on carbonisation behaviour of low rank coal briquettes in a pilot-scale coke oven.

^{[14]}The present study develops an integrated numerical model for the optical-thermal-fluid-mechanical analysis of PTRs by coupling Monte Carlo ray-tracing method, finite volume method, and finite element method.

^{[15]}This study developed an integrated numerical model to simulate the wave-monopile-seabed interaction considering a nonlinear contact at the pile-soil interface.

^{[16]}In this paper, an integrated numerical model is proposed to examine the wave and current-induced pore pressure generation, for instance, oscillatory and residual pore pressure, around a buried pipeline.

^{[17]}In this study, a three-dimensional (3D) integrated numerical model consisting of a wave submodel and seabed submodel was adopted to investigate the wave–structure–seabed interaction.

^{[18]}An integrated numerical model is established with considering detailed heat transfer and fluid flow in the melting furnace, as well as discrete bubble tracking in molten quartz.

^{[19]}The research presented in this paper deals with the development of an integrated numerical model for the estimation of the incremental surface wear and damage accumulation in linear slide rails.

^{[20]}The numerical crop growth model Italian Vineyard Integrated Numerical model for Estimating physiological values (IVINE) was developed in order to evaluate environmental forcing effects on vine growth.

^{[21]}Subsequently, an integrated numerical model based on multiple consecutive steps is established to characterize the damage accumulation and failure mechanisms of FMLs, in which a user defined subroutine VUMAT, is developed to consider the stiffness degradation and damage evolution of composite material.

^{[22]}An integrated numerical model was built to predict the quenching and the subsequent cold rolling processes.

^{[23]}An integrated numerical model has been developed based on the General Transport Equation Analysis code.

^{[24]}In this paper, preliminary study is conducted on oscillatory wave-induced seabed response around three configuration cases of pile support foundations applying a 3-dimensional integrated numerical model to study and comparatively analyzed them.

^{[25]}In this paper, to reveal the physics behind sediment incipient motion around a free spanning pipeline, an integrated numerical model, coupling the SST (Shear-Stress Transport) turbulence model with the porous seabed model, was proposed.

^{[26]}We have to develop an integrated numerical model to support policymaking for coastal environment development and conservation.

^{[27]}The present work deals with the development of an integrated numerical model able to simulate the manufacturing route for formed thin sheets, rolled, welded by friction stir welding (FSW) technology and finally shaped by means of a single point incremental forming (SPIF) process.

^{[28]}” We show how it was useful for us to consider different outputs of the project, in particular our integrated numerical model, as snapshots of epistemic processes supporting interdisciplinary exchange rather than purely as research products.

^{[29]}

## integrated numerical simulation

This paper presents a mix design approach based on integrated numerical simulation of heat transfer in concrete and genetic algorithm optimisation that minimises the risk of early-age cracking within the limits specified for the mechanical performance of concrete.^{[1]}The design driven by integrated numerical simulations encompassing from production to the long-term performance is already ordinary in the manufacturing of plastic and metallic parts.

^{[2]}Integrated numerical simulations are conducted to study the structural deformation and energy absorption of the striking ship and the struck pontoon.

^{[3]}Geostatistical three-dimensional (3-D) models and an integrated numerical simulation were constructed to quantify the geometry, spatial distribution and continuity of the reservoir sands and to predict the remaining oil distribution rules.

^{[4]}To evaluate public health impacts of wildfire smoke, we integrated numerical simulations and observations for regional fire events during August-September of 2017.

^{[5]}Integrated numerical simulations are conducted to study the structural deformation of the pontoon wall during the collision.

^{[6]}

## integrated numerical approach

In this work, an integrated numerical approach for predicting the damage mechanism of unidirectional CFRP composites at the micro-scale level has been developed using a multi-scale modeling strategy, where the curing residual stresses induced in autoclave curing process is taken into account.^{[1]}The integrated numerical approach implemented in the FE software via user defined subroutines can simulate the morphology and size distribution of constituent grains, transformed fractions of various phases, hardness profiles and flow stresses after thermo-mechanical process with large plastic deformation.

^{[2]}In order to investigate how ultimate strength and endurance limit of an exemplary PRMMC material, WC-20 wt% Co, are related to other structural and mechanical characteristics, an integrated numerical approach consisting of direct methods (DM) and artificial neural network (ANN) is presented in this work.

^{[3]}For solving the inherent energy simulation problem, the integrated numerical approach based on the simplified one-dimensional nodal thermal model and the optical model was proposed.

^{[4]}We present a newly developed integrated numerical approach, which combines the time-dependent RANS method in predicting the temporal and spatial evolution of a heavy gas turbulent dispersion with the macroscopic model of a crowd movement.

^{[5]}

## integrated numerical modelling

An integrated numerical modelling of discrete element method (DEM) and computational fluid dynamics (CFD) are applied.^{[1]}INMOST (Integrated Numerical Modelling Object-oriented Supercomputing Technologies) is a programming platform which facilitates development of parallel models.

^{[2]}This work describes integrated numerical modelling applied to DEMO discharges with tungsten wall and divertor, using the COREDIV code, which self-consistently solves 1D radial transport equations of plasma and impurities in the core region and 2D multi-fluid transport in the SOL.

^{[3]}In order to evaluate and understand the disaster chain effect linked to the potentially unstable rock mass, we systematically studied the multi-hazard scenarios through an integrated numerical modelling approach.

^{[4]}

## integrated numerical method

In this paper, a multi-physics integrated numerical method of a dry sump transmission, considering a system approach is presented.^{[1]}In this paper, an integrated numerical method is established to predict the strain sensing behavior of PPy-coated flexible conductive fibers.

^{[2]}An integrated numerical method, which couples a seakeeping solver and a Navier-Stokes (NS) solver with the volume of fluid (VOF) model, has been developed to study the behavior of a damage ship in waves.

^{[3]}

## integrated numerical computing

The current study aims to design an integrated numerical computing-based scheme by applying the Levenberg–Marquardt backpropagation (LMB) neural network to solve the nonlinear susceptible (S), infected (I) and recovered (R) (SIR) system of differential equations, representing the spreading of infection along with its treatment.^{[1]}In the present investigation, design of integrated numerical computing through Levenberg-Marquardt backpropagation neural network (LMBNN) is presented to examine the fluid mechanics problems governing the dynamics of expanding and contracting cylinder for Cross magneto-nanofluid flow (ECCCMNF) model in the presence of time dependent non-uniform magnetic force and permeability of the cylinder.

^{[2]}The design of integrated numerical computing through back-propagated neural networks with Levenberg-Marquard system (BNN-LMS) is presented to explore the fluid mechanics problems governing the system of heat transfer between two porous parallel plates of steady nanofluids (HTPSNF) under the stimulus of thermophoretic and Brownian motion.

^{[3]}

## integrated numerical scheme

For this purpose, we develop an integrated numerical scheme accounting for roughness effects by coupling a modified lattice spring model (LSM) with discrete fracture networks (DFNs).^{[1]}We tackle this mathematical model numerically with fully adaptive and integrated numerical schemes tailored to the simulation of variable density multiphase flows governed by diffuse interface models.

^{[2]}