Pure Advection Research Articles

Extremization to fine tune physics informed neural networks for solving boundary value problems

We propose a novel method for fast and accurate training of physics-informed neural networks (PINNs) to find solutions to boundary value problems (BVPs) and initial boundary value problems (IBVPs). By combining the methods of training deep neural networks (DNNs) and Extreme Learning Machines (ELMs), we develop a model which has the expressivity of DNNs with the fine-tuning ability of ELMs. We showcase the superiority of our proposed method by solving several BVPs and IBVPs which include linear and non-linear ordinary differential equations (ODEs), partial differential equations (PDEs) and coupled PDEs. The examples we consider include a stiff coupled ODE system where traditional numerical methods fail, a 3+1D non-linear PDE, Kovasznay flow and Taylor–Green vortex solutions to incompressible Navier–Stokes equations and pure advection solution of 1+1 D compressible Euler equation.The Theory of Functional Connections (TFC) is used to exactly impose initial and boundary conditions (IBCs) of (I)BVPs on PINNs. We propose a modification to the TFC framework named Reduced TFC and show a significant improvement in the training and inference time of PINNs compared to IBCs imposed using TFC. Furthermore, Reduced TFC is shown to be able to generalize to more complex boundary geometries which is not possible with TFC. We also introduce a method of applying boundary conditions at infinity for BVPs and numerically solve the pure advection in 1+1 D Euler equations using these boundary conditions.

Are odd radio circles virial shocks around massive galaxies? Implications for cosmic-ray diffusion in the circumgalactic medium

ABSTRACT Recently, a new population of circular radio (∼GHz) objects has been discovered at high Galactic latitudes, called the odd radio circles (ORCs). A fraction of the ORCs encircles massive galaxies in the sky with stellar mass ∼1011 M⊙ situated at z = 0.2–0.6, suggesting a possible physical connection. In this paper, we explore the possibility that these radio circles originate from the accretion shocks/virial shocks around massive (${\gtrsim} 10^{13}\, \ {\rm M}_\odot$) dark matter halo at z ∼ 0.5. We found that the radio flux density of the emitting shell is marginally consistent with the ORCs. We also find that pure advection of electrons from the shock results in a radio-emitting shell that is considerably narrower than the observed one due to strong inverse-Compton cooling of electrons. Instead, we show that the diffusion of cosmic-ray (CR) electrons plays a significant role in increasing the width of the shell. We infer a diffusion coefficient, $D_{\rm cr} \sim 10^{30}\ {\rm cm^2\, s^{-1}}$, consistent with the values expected for low-density circumgalactic medium (CGM). If ORCs indeed trace virial shocks, then our derived CR diffusion coefficient represents one of the few estimations available for the low-density CGM. Finally, we show that the apparent discrepancy between ORC and halo number density can be mitigated by considering an incomplete halo virialization and the limited radiation efficiency of shocks. This study therefore opens up new avenues to study such shocks and non-thermal particle acceleration within them. Furthermore, our results suggest that low-mass galaxies (≲1013 M⊙) may not show ORCs due to their significantly lower radio surface brightness.

A novel steepness-adjustable harmonic volume-of-fluid method for interface capturing

The algebraic volume-of-fluid (VOF) method based on the construction strategy of switching technique has received extensive attention recently. However, all the previous algebraic VOF methods were constructed by combining different methods of compressible differencing scheme (CDS) and the high resolution scheme (HRS), which would switch back and forth in most cases. Thus the final algebraic VOF method usually becomes to be complicated, and the numerical instabilities would be increased. In this paper, a novel algebraic VOF method, without the operations of switching back and forth, is constructed within a unified framework of the steepness-adjustable harmonic (SAH) scheme (He et al. (2022) [33]). A thorough validation of the present method is conducted, examining the pure advection of the interface indicator function. The results indicate that the present method can resolve the interface capturing with substantially low numerical diffusion and low numerical oscillations.

An accretion‐jet model for 3C 84: Interpreting the spectral energy distribution and Faraday rotation measure

Abstract3C 84 is a well‐known supermassive black hole that can be used to explore jet and accretion physics. In this work, we model the multiwavelength spectral energy distribution (SED) of the 3C 84, and find that the SED is difficult to fit with pure advection dominated accretion flow (ADAF) or pure jet model. Using a coupled ADAF‐jet model to fit the SED of 3C 84, it is found that the radio emission and the millimeter emission can be naturally reproduced by the synchrotron radiation of nonthermal electrons in the jet, and that the X‐ray emission may predominantly come from inverse Compton radiation from electrons in ADAF. According to the Rotation Measure (RM) obtained by the polarization observation, we consider the possible location of the polarizing source and found that the calculated RM in the jet is roughly consistent with the observational constraints. These results will help us better understand jets produced by black holes.

A new open-source library based on novel high-resolution structure-preserving convection schemes

This work develops a new finite volume convection scheme and open-source library for convection-dominated problems on unstructured grids. The formulated reconstruction operators can realize high-resolution and structure-preserving properties by adjusting numerical dissipation and anti-dissipation errors in a unified normalized-variable diagram. Then, this work develops a new open-source library based on the devised schemes within one of the most widely used general-purpose open-source software whose solution quality is intrinsically limited by the low accuracy of the conventional total variation diminishing schemes. The performance of the new library is first verified by some fundamental problems including pure advection and inviscid Euler equations. The numerical results of the accuracy tests show that the developed interpolation library can significantly reduce numerical errors with a minor increased computational cost compared with the conventional second-order schemes. The complex profile advection test demonstrates that the new library can offer an improved structure-preserving property that gives essentially oscillation-free solutions and preserves the structures of the passive transported scalar. Furthermore, the robustness of the new library is validated by compressible high-speed flow simulations with irregular geometries. Thus, this work presents a new library of high-resolution structure-preserving schemes for the accurate and efficient discretization of the convection term which plays an essential role in a wide range of computational fluid dynamics. The source code of the new scheme and library are released via DOI:10.5281/zenodo.8399000.

Extending the isoAdvector Geometric VOF Method to Flows in Porous Media

We consider the interfacial flow in and around porous structures in coastal and marine engineering.* During recent years, interfacial flow through porous media has been repeatedly simulated with Computational Fluid Dynamics (CFD) based on algebraic Volume Of Fluid (VOF) methods [1] [2]. Here, we present an implementation of a porous medium interfacial flow solver based on the geometric VOF method, isoAdvector [3] [4]. In our implementation, the porous medium is treated without resolving the actual pore geometry. Rather, the porous media, pores, and rigid structure are considered a continuum and the effects of porosity on the fluid flow are modelled through source terms in the Navier-Stokes equations, including Darcy-Forchheimer forces, added mass force and accounting for the part of mesh cells that are occupied by the solid material comprising the skeleton of the porous medium. The governing equations are adopted from the formulation by Jensen et al. [1]. For the interface advection using isoAdvector, we also account for the reduced cell volume available for fluid flow and for the increase in the interface front velocity caused by a cell being partially filled with solid material. The solver is implemented in the open source CFD library OpenFOAM®. It is validated using two case setups: 1) A pure passive advection test case to compare the isolated advection algorithm against a known analytical solution and 2) a porous dam break case by Liu et al. [5] where both numerical and experimental results are available for comparison. We find good agreement with numerical and experimental results. For both cases the interface sharpness, shape conservation as well as volume conservation and boundedness are demonstrated to be very good. The solver is released as open source for the benefit of the coastal and marine CFD community (code repository https://github.com/InterFlowers/porousInterIsoFoam) and as of OpenFOAM-v2112 the new functionality is integrated in the official interIsoFoam solver. * This article is an updated version of the conference paper Missios et al. 2022 [6] presented at the Marine2021 conference.

Time‐continuous and time‐discontinuous space‐time finite elements for advection‐diffusion problems

AbstractWe construct four variants of space‐time finite element discretizations based on linear tensor‐product and simplex‐type finite elements. The resulting discretizations are continuous in space, and continuous or discontinuous in time. In a first test run, all four methods are applied to a linear scalar advection‐diffusion model problem. Then, the convergence properties of the time‐discontinuous space‐time finite element discretizations are studied in numerical experiments. Advection velocity and diffusion coefficient are varied, such that the parabolic case of pure diffusion (heat equation), as well as, the hyperbolic case of pure advection (transport equation) are included in the study. For each model parameter set, the error at the final time is computed for spatial and temporal element lengths ranging over several orders of magnitude to allow for an individual evaluation of the methods' spatial, temporal, and space‐time accuracy. In the parabolic case, particular attention is paid to the influence of time‐dependent boundary conditions. Key findings include a spatial accuracy of second order and a temporal accuracy between second and third order. The temporal accuracy tends toward third order depending on how advection‐dominated the test case is, on the choice of the specific discretization method, and on the time‐(in)dependence and treatment of the boundary conditions. Additionally, the potential of time‐continuous simplex space‐time finite elements for heat flux computations is demonstrated with a piston ring pack test case and a subtractive manufacturing test case.

Under What Conditions Does Transverse Macrodispersion Exist in Groundwater Flow?

AbstractIn recent years there has been vigorous debate whether asymptotic transverse macrodispersion exists in steady three‐dimensional (3D) groundwater flows in the purely advective limit. This question is tied to the topology of 3D flow paths (termed the Lagrangian kinematics), specifically whether streamlines can undergo braiding motions or can wander freely in the transverse direction. In this study we determine which Darcy flows do admit asymptotic transverse macrodispersion for purely advective transport on the basis of the conductivity structure. We prove that porous media with smooth, locally isotropic hydraulic conductivity exhibit zero transverse macrodispersion under pure advection due to constraints on the Lagrangian kinematics of these flows, whereas either non‐smooth or locally anisotropic conductivity fields can generate transverse macrodispersion. This has implications for upscaling locally isotropic porous media to the block scale as this can result in a locally anisotropic conductivity, leading to non‐zero macrodispersion at the block scale that is spurious in that it does not arise for the fully resolved Darcy scale flow. We also show that conventional numerical methods for computation of particle trajectories do not explicitly preserve the kinematic constraints associated with locally isotropic Darcy flow, and propose a novel psuedo‐symplectic method that preserves these constraints. These results provide insights into the mechanisms that govern transverse macrodispersion in groundwater flow, and unify seemingly contradictory results in the literature in a consistent framework. These insights call into question the ability of smooth, locally isotropic conductivity fields to represent flow and transport in real heterogeneous porous media.

Modified far-upwind reconstruction methods for the implementation of NVSF schemes on unstructured grids

Based on the analysis of the existing far-upwind reconstruction methods, three modified far-upwind reconstruction methods, named as NM-1, NM-2 and NM-3, are developed for the implementation of Normalized Variable and Space Formulation (NVSF) schemes on arbitrary unstructured grids. In the modified reconstruction methods, the locations of the cell centroids around the upwind cell are considered for the position reconstruction. And three interpolation techniques, including the nearest point interpolation, the inverse distance weighted interpolation and the gradient-considered inverse distance weighted interpolation are adopted for the value reconstruction. Moreover, a modified boundedness limitation is proposed to constrain the reconstructed value of the far-upwind node within a more reasonable scope. The pure advection tests demonstrate that NM-3 leads to a better overall performance in terms of accuracy and convergence comparing with the previous and the other modified reconstruction methods for seven classic NVSF schemes. Such advantage of NM-3 retains in the applications of multiphase flow (dam-break flow) and incompressible fluid flow (backward step flow and lid-driven cavity flow). Theoretical analysis implies that the good performance of NM-3 mainly attributes to that its position reconstruction better represents the ‘average position’ of the adjacent cell centroids around the upwind cell and its value reconstruction combines the advantages of the nearest point interpolation and the inverse distance weighted interpolation simultaneously.

A density-constrained model for chemotaxis

We consider a model of congestion dynamics with chemotaxis: the density of cells follows a chemical signal it generates, while subject to an incompressibility constraint. The incompressibility constraint results in the formation of patches, describing regions where the maximal density has been reached. The dynamics of these patches can be described by either Hele-Shaw or Richards equation type flow (depending on whether we consider the model with diffusion or the model with pure advection). Our focus in this paper is on the construction of weak solutions for this problem via a variational discrete time scheme of JKO type. We also establish the uniqueness of these solutions. In addition, we make more rigorous the connection between this incompressible chemotaxis model and the free boundary problems describing the motion of the patches in terms of the density and associated pressure variable. In particular, we obtain new results characterising the pressure variable as the solution of an obstacle problem and prove that in the pure advection case the dynamic preserves patches.

Linear Stochastic Analysis of the Partial Reversibility of Ensemble and Effective Dispersion in Heterogeneous Porous Media

AbstractMacrodispersion in heterogeneous formations is caused by spatial variability of the velocity field, making different parts of a plume experience different advective displacements. Differential advection interacts with diffusion, which hardly affects longitudinal ensemble dispersion (i.e., the spread of the ensemble‐averaged concentration) but determines effective dispersion, that is, the expected spread of individual plumes for point injections. The latter has been suggested as metric of solute mixing. Pure advection is fully reversible, whereas diffusion is completely irreversible. We quantify the partial reversibility of macrodispersion by analyzing the second central ensemble and effective spatial moments for advective‐diffusive transport in heterogeneous domains with flow reversal, applying linear stochastic theory to approximate the corresponding moments and comparing them to particle‐tracking random‐walk simulations in periodic media. Diffusion causes solute particles to deviate from their forward trajectories when flow is reversed. As long as advective memory dominates, both types of second central moments decrease during backward motion, then reach a minimum, and increase again. The reversibility is considerably bigger for ensemble than effective dispersion but the latter also shows partial reversibility, challenging its use as metric of mixing. The stronger diffusion is in comparison to advection, the less reversible dispersion becomes. After equally long times of forward and backward motion, the two types of second central moments differ, but to a much smaller extent than in pure forward motion. In realistic settings, the advective memory affects dispersion so strongly that the asymptotic regime is not reached before the plume center has returned to its origin.

A closer look at supernovae as seeds for galactic magnetization

Context. Explaining the currently observed magnetic fields in galaxies requires relatively strong seeding in the early Universe. One of the current theories proposes that magnetic seeds on the order of μG were expelled by supernova (SN) explosions after primordial fields of nG strength or weaker were amplified in stellar interiors. Aims. In this work, we take a closer look at this theory and calculate the maximum magnetic energy that can be injected in the interstellar medium by a stellar cluster of mass Mcl based on what is currently known about stellar magnetism. Methods. We consider early-type stars and adopt either a Salpeter or a top-heavy initial mass function. For their magnetic fields, we adopt either a Gaussian or a bimodal distribution. The Gaussian model assumes that all massive stars are magnetized with 103 < ⟨B*⟩< 104 G, while the bimodal, consistent with observations of Milky Way stars, assumes only 5 − 10% of OB stars have 103 < ⟨B*⟩< 104 G, while the rest have 10 < ⟨B*⟩< 102 G. We ignore the effect of magnetic diffusion and assume no losses of magnetic energy. Results. We find that the maximum magnetic energy that can be injected by a stellar population is between 10−10 and 10−7 times the total SN energy. The highest end of these estimates is about five orders of magnitude lower than what is usually employed in cosmological simulations, where about 10−2 of the SN energy is injected as magnetic. Conclusions. Pure advection of the stellar magnetic field by SN explosions is a good candidate for seeding a dynamo, but not enough to magnetize galaxies. Assuming SNe as the main mechanism for galactic magnetization, the magnetic field cannot exceed an intensity of 10−7 G in the best-case scenario for a population of 105 solar masses in a superbubble of 300 pc radius, while more typical values are between 10−10 and 10−9 G. Therefore, other scenarios for galactic magnetization at high redshift need to be explored.

Modelling grain-size distributions in C-type shocks using a discrete power-law model

In this paper we discuss the implementation of a discrete, piecewise power-law grain-size distribution method into a numerical multifluid MHD code as described in Sumpter and Van Loo (2020). Such a description allows to capture the full size range of dust grains and their dynamical effects. The only assumptions are that grains within a single discrete bin have the same velocity and charge. We test the implementation by modelling plane-parallel C-type shocks and compare the results with shock models of multispecies grain models. We find that both the discrete and multispecies grain models converge to the same shock profile. However, the convergence for the discrete models is faster than for the multispecies grain models. For the pure advection models a single discrete bin is sufficient, while the multispecies grain models need a minimum of 8 grain species. When including grain sputtering the necessary number of discrete bins increases to 4, as the grain distribution cannot be described by a single power-law as in the advection models. The multispecies grain models still need more grain species to model the distribution, but the number does not increase compared to the pure advection models. Our results show that modelling the grain distribution function using a discrete distribution reduces the computational cost needed to capture the grain physics significantly.

Breaking wave simulations for a high-speed surface vessel with hybrid THINC and HRIC schemes

To simulate the ship-induced breaking waves with high-accuracy VOF (volume of fluid) schemes, the unstructured THINC (tangent of hyperbola for interface capturing) type scheme was selected as the main interface capturing method.Particularly, an extension version of THINC/QQ (THINC method with quadratic surface representation and Gaussian quadrature), namely THINC/QQ-SF (THINC/QQ extended for split-face unstructured cells) was used. The computational domain was discretized by the trimmed meshes of STAR-CCM+. The mesh cells were categorized into three groups, including regular unstructured (i.e. hexahedral, tetrahedral, prismatic and pyramidal) cells, split-face unstructured cells and polyhedral cells. THINC/QQ-SF was applied for the first two cell groups, which take up most of the space. The algebraic VOF scheme of HRIC (high-resolution interface capturing) which has the advantage of algorithm simplicity, was implemented for the third cell group. To validate the performance of THINC/QQ-SF and HRIC, a series of testing meshes were designed for the pure VOF advection cases. Additionally, the geometric VOF scheme of isoAdvector was also involved for comparisons. In terms of the accuracy, THINC/QQ-SF is similar with isoAdvector, both of which are much better than HRIC. For the efficiency, both THINC/QQ-SF and HRIC have obvious advantages over isoAdvector under the present conditions. Then, the hull form of DTMB (David Taylor model basin) 5415 was chosen for testing, under the Froude number of 0.35. By using the combination of THINC/QQ-SF and HRIC (i.e. THINC/QQ-SF & HRIC), the compactness of the interface can be maintained. Besides, the wave elevations are well agreed with the published experiment. For the averaged calm-water resistance, the present strategy can obtain more accurate results with fewer (or much fewer) cells, compared with the previous CFD studies. To better show the advantages of the hybrid method, the simulations with pure HRIC were also conducted. Compared with pure HRIC, THINC/QQ-SF & HRIC can better capture the wave breaking details with less numerical diffusion, and the reliability of the resistance prediction is higher.

A Massively Parallel Eulerian-Lagrangian Method for Advection-Dominated Transport in Viscous Fluids

Motivated by challenges in Earth mantle convection, we present a massively parallel implementation of an Eulerian-Lagrangian method for the advection-diffusion equation in the advection-dominated regime. The advection term is treated by a particle-based, characteristics method coupled to a block-structured finite-element framework. Its numerical and computational performance is evaluated in multiple, two- and three-dimensional benchmarks, including curved geometries, discontinuous solutions, pure advection, and it is applied to a coupled non-linear system modeling buoyancy-driven convection in Stokes flow. We demonstrate the parallel performance in a strong and weak scaling experiment, with scalability to up to $147,456$ parallel processes, solving for more than $5.2 \times 10^{10}$ (52 billion) degrees of freedom per time-step.

Analysis of thermal dilution experiments with distributed temperature sensing for fractured rock characterization

Thermal dilution experiments with Fiber-Optic Distributed Temperature Sensing (FO-DTS) were conducted at the In-situ Stimulation and Circulation (ISC) rock laboratory, at the Grimsel Test Site (GTS) in Switzerland. The experiment consists in replacing the total volume of a borehole with a warmer water and monitoring the rate of temperature increase and decrease during the heating and cooling periods, respectively. The changes in temperature monitored in depth and time under various hydraulic conditions and in different boreholes, are used to investigate the information provided by thermal dilution experiments in terms of groundwater flow and thermal properties in low-permeable fractured crystalline rock. The data analysis, and the use of analytical and numerical solutions for reproducing this data in the context of pure diffusion and advection–diffusion scenarios, lead to the following improvements and conclusions. (i) The formation thermal conductivity is estimated along the borehole by inverting the data collected under ambient conditions with a simple analytical solution. The estimated values are consistent with laboratory estimates. The method presents the advantage of requiring much shorter experiments than existing methods based on standard active-line-source (ALS) experiments, i.e., several hours versus the traditional 1–2 days. (ii) Hydraulically active fractures connecting boreholes are detected from experiments conducted under cross-borehole forced hydraulic conditions. (iii) The formation thermal conductivity and fracture flow velocity have a distinguished impact on the temperature anomalies for some ranges of these property values, implying that both properties can be estimated from well-parametrized experiments.

Quantifying the Effects of Bed Roughness on Transit Time Distributions via Direct Numerical Simulations of Turbulent Hyporheic Exchange

AbstractWe report direct numerical simulation (DNS) results of hyporheic exchange for a flat river bed with two different particle roughness textures, at a surface flow friction Reynolds number of 395 and a bed permeability Reynolds number of 2.6. Transit time distributions (TTDs), subsurface flow patterns, and the interfacial volumetric fluxes are discussed. The transit time was quantified using a forward particle tracking method based on pure advection by three‐dimensional, pore‐resolved, time‐mean velocities. Results show that bed roughness induces deep subsurface flow paths that yield a TTD with a power‐law tail. Roughness obstructs the surface flow, creating interfacial pressure variations which induce subsurface flow. Next, the molecular diffusion is accounted for based on a random walk method and is shown to increase transit times regardless of roughness texture. This work demonstrates that particle roughness on a macroscopically flat sediment bed can induce significant hyporheic exchange that is fundamentally similar to that induced by bedforms.

GPU implementation of Explicit and Implicit Eulerian methods with TVD schemes for solving 2D solute transport in heterogeneous flows

In this work we present an efficient implementation of Eulerian TVD methods. We apply parallelization strategies based entirely on GPU for the solution of the 2D transport equation in heterogeneous porous media. Additionally, a parallel strategy is proposed for the generation of exponentially correlated lognormally distributed permeability fields in GPU. The programs are developed using C++/CUDA. The implemented methods are used to solve advective dominant problems, in a context of Monte Carlo type simulations to numerically determine the longitudinal and transversal macrodispersion coefficients averaging over 100 simulations for permeability fields for a large range of variances. The following types of transport are considered for testing: pure advection, advection-diffusion and advection-dispersion. The performance in terms of the computation time of explicit and implicit methods are compared. We show that the implemented algorithms allow to efficiently solve problems in computational domains of up to 134.5 million cells in a single GPU.

Mass Advection–Diffusion in Creeping Flow Through an Orifice Plate: A Model for Nanoporous Atomically Thin Membranes

Abstract Continuum transport equations are commonly applied to nanopores in atomically thin membranes for simple modeling. Although these equations do not apply for nanopores approaching the fluid or solute molecule size, they can be reasonably accurate for larger nanopores. Relatively large graphene nanopores have applications in small particle filtration and appear as unwanted defects in large-area membranes. Solute transport rates through these nanopores determine the rejection performance of the membrane. Atomically thin membranes commonly operate in a regime where advection and diffusion both contribute appreciably to transport. Solute mass transfer rates through larger nanopores have previously been modeled by adding continuum estimates for pure diffusion and pure advection through an infinitesimally thick orifice plate, as if the separate contributions were independent. We show here that estimating the transport rate in this way is accurate to within 30%. We further derive an expression for the net mass transfer rate in advection–diffusion through an infinitesimal thickness orifice plate at low Reynolds numbers that is accurate to within 1% for positive Péclet numbers (where diffusion is in the same direction as advection) and applies for negative Péclet numbers as well. Based on our expression, we devise an equation for the net mass transfer rate in creeping flow through orifice plates of arbitrary thickness that matches finite volume calculations to within 3% for positive Péclet numbers. These simple but accurate analytical equations for mass transfer rates in creeping flow through an orifice plate are useful tools in constructing approximate transport models.

Analysis of fabrication and crack-induced porosity migration in mixed oxide fuels for sodium fast reactors by the finite element method

We present an engineering-scale model for the migration of porosity in a fuel pellet experiencing a temperature gradient. The system of coupled pore advection and heat diffusion equations governing the problem is solved by a fixed-point iteration technique. The coupling between porosity and temperature fields is considered via the dependency of pore advection velocity on the local temperature and temperature gradient, and via the dependency of fuel thermal conductivity and of the volumetric power source on the local porosity. We employ the finite element method to discretize the resulting equations. As pure advection solutions obtained by this method are well-known to present spurious spatial oscillations, we introduce stabilization techniques in the pore advection equation. The proposed model is first tested against a benchmark problem representative for the conditions of an uranium-plutonium oxide fuel pellet irradiated in a sodium fast reactor. The results are compared to the those obtained by a model implemented in the BISON fuel performance code. The analysis shows how the results of the newly developed model are in line with those obtained by the reference model, and underlines a superior stability of the solution. The model is then applied to analyze the contribution of as-fabricated and crack-induced porosities in determining the fuel restructuring and in particular the central hole formation. A comparison to experimental data shows the impact of considering crack-induced porosity to predict the extent of the central void.