This paper presents a numerical method for calculating anisotropic radiative intensities on a spherical capsule within a cylindrical hohlraum. The combination of capsule and hohlraum is the typical configuration in the indirectly driven inertial confinement fusion (ICF). The hohlraum is irradiated by lasers and thus generates an anisotropic radiative field around the capsule. The radiative energy flux along the hohlraum inner surface is firstly computed by utilizing the conventional view factor formulation. Anisotropic radiative intensities on the capsule are then obtained from the Lambertian approximation. A numerical example calibrated by experimental radiation temperature is further provided to demonstrate the anisotropy of radiative intensities in ICF. Program summary Program Title: ViewaCPC Library link to program files: https://doi.org/10.17632/hngb5z2m2x.1Licensing provisions: GPLv3Programming language: M languageNature of problem: In order to assess the radiative drive symmetry in the indirectly driven ICF, it is necessary to compute radiative intensities on the capsule. Moreover, the capsule-only simulation of the indirectly driven ICF with the radiation transport equation requires radiative intensities on the capsule as boundary conditions. However, it is difficult to calculate the radiative intensity at a given location on the capsule in a given direction.Solution method: We firstly compute the radiative energy flux along the hohlraum inner surface by using the view factor method. The radiative intensities on the capsule are then calculated from the Lambertian approximation.Additional comments including restrictions and unusual features: Due to the low density of the filling gas between the capsule and the hohlraum, the radiative intensity slightly attenuates when propagating from the hohlraum inner surface to the capsule surface. And the view factor method is computationally efficient. Hence the introduced method can specify radiative intensities accurately and efficiently. But two dimensional rotational symmetry is assumed in this paper, and some parameters need to be calibrated by experimental radiation temperature.
The self-organised morphogenesis of multicellular organisms emerges not only from biochemical but also from mechanical processes operating across spatial scales. Yet, computational tools for simulating tissue-scale mechanics have largely been released as restricted, study-specific codes. Here, we present NewtonBioMorphX, a GPU-accelerated, open-access comprehensive framework for simulating tissue-scale mechanical morphogenesis. Built on a finite-strain finite-element formulation on tetrahedral meshes, the software implements an unusually broad set of mechanical ingredients: isotropic and anisotropic (direction-specific) growth; multi-layer tissue mechanics; neo-Hookean hyperelasticity combined with stretch-based plasticity; Kelvin–Voigt viscoelasticity; passive anisotropic fibres emulating 3D collagen networks; anisotropic active contractile filaments emulating actin; Hertzian contact forces; and multiple orthonormal coordinate bases (Cartesian, normal–tangent, cylindrical, spherical, cone-adapted, and toroidal). Equally central is an extensive, user-friendly graphical interface spanning the entire workflow — mesh generation from geometric primitives or arbitrary mesh input, per-layer material and growth specification (including analytical functions of space and time compiled at runtime), boundary-condition assignment, real-time colour-mapped and glyph-based visualisation of scalar and tensor fields, and structured data export — allowing intricate mechanical modelling of morphogenetic processes without editing or recompiling source code. The NewtonBioMorphX framework is validated using a benchmark implementing the well-known Cook’s membrane problem, and its versatility is illustrated through parameter gradient plots, as well as twelve ready-to-run preset examples spanning diverse morphologies.PROGRAM SUMMARYProgram title: NewtonBioMorphXDeveloper’s repository link: https://github.com/LANEvol/NewtonBioMorphXSoftware webpage link: https://www.lanevol.org/projects/NewtonBioMorphXLicensing provisions: GNU General Public Licence 3 (GPL-3.0)Programming language: C++, NVIDIA® CUDA®Nature of problem: Morphogenesis arises from coupled biochemical and mechanical processes acting in cells and tissues. Cell division, cell rearrangements and cellular forces —such as cytoskeletal activity and cell-cell adhesion— scale up to multiple tissue-level behaviours including, but not limited to, growth, convergent extension, and buckling. Capturing these non-linear, multiscale tissue deformations requires continuum models. Yet, existing tools remain fragmented and study-specific, lacking an accessible, unified simulation framework.Solution method: NewtonBioMorphX addresses this need by providing a GPU-accelerated finite-element framework for simulating hyperelastic, plastic, and viscous tissues with growth, anisotropic passive fibres, and active stresses. It integrates a broad set of functionalities into a single platform with mesh handling, material assignment, boundary-conditions, visualisation tools, and efficient GPU solvers, enabling researchers to model diverse morphogenetic processes through an accessible graphical interface. Executables are provided for Windows and Linux while the compilation of source code is facilitated by the use of Docker Engine tools.
We introduce AFiD-2phaseDarcy, an efficient, open-source and massively parallelized finite-difference solver tailored for large-scale simulations of buoyancy-driven incompressible multiphase convection in porous media. Built within the well-established AFiD framework, the solver extends the original wall-bounded buoyancy-driven convection code to handle fully coupled multiphase Darcy momentum transport, saturation and scalar transport equations. Spatial operators are discretized using finite-difference schemes, while temporal integration is performed using a low-storage third-order Runge–Kutta scheme combined with a Crank–Nicolson formulation for implicit terms. To alleviate the computational bottleneck associated with pressure–velocity coupling, a fractional-step projection method is employed. The resulting global variable-coefficient Poisson equation is decomposed using a pressure-splitting approach and solved using a Fast Fourier Transform (FFT)-based algorithm, substantially reducing parallel communication overhead. The numerical accuracy of AFiD-2phaseDarcy is rigorously verified against a series of benchmark cases, including canonical single-phase porous-media convection, isothermal two-phase flow and multiphase thermal convection. Performance benchmarks demonstrate that the proposed FFT-based pressure-splitting solver achieves an approximately fivefold computational speedup over the conventional monolithic direct solver implemented using the parallel PETSc framework, while maintaining comparable computational accuracy. Furthermore, distributed strong-scaling tests on the SCNet platform demonstrate near-linear speedup and high parallel efficiency on up to 2000 CPU cores. This open-source framework provides an efficient numerical tool for large-scale simulations of subsurface transport processes, with potential applications including geological carbon sequestration and geothermal energy exploitation.PROGRAM SUMMARYProgram Title: AFiD-2phaseDarcyCPC Library link to program files: https://doi.org/10.17632/2g7v8hvjry.1Developer’s repository link: https://github.com/duxcfd-ustc/AFiD-2phaseDarcyLicensing provisions: CC BY 4.0Programming language: FORTRAN 90, MPINature of problem: Solving the nonlinear coupled equations governing buoyancy-driven incompressible multiphase convection in porous media based on the multiphase Darcy law, saturation and scalar transport equations. The computational domain is a rectangular box bounded by rigid, impermeable walls at the top and bottom, with periodic boundary conditions imposed in the horizontal directions.Solution method: Spatial operators are discretized using finite-difference schemes. Temporal integration is performed using a low-storage third-order Runge–Kutta scheme combined with a Crank–Nicolson formulation for implicit terms. A fractional-step projection method is employed to resolve the pressure–velocity coupling. The resulting global variable-coefficient pressure Poisson equation is decomposed using an advanced pressure-splitting method and efficiently solved through line-by-line one-dimensional FFT-based algebraic systems. Highly scalable parallel performance is achieved using a 2-D pencil-decomposition MPI architecture implemented within the open-source AFiD framework.
Conventional simulation approaches face difficulties for massive particle motion and efficient methods are urgently in need. A Fourier-featured physics informed neural network (FF-PINN) framework is developed for efficient particle resolved simulation of acoustic agglomeration (AA). The method replaces repeated evaluation of the sound pressure gradient force (SPGF) and Stokes drag with pretrained neural surrogates constructed from governing equations. The acoustics force field is decomposed into spatial and temporal components and learned through dedicated subnetworks with Fourier feature encoding, while a separate network captures the velocity dependent drag contribution. Validation against finite element method (FEM) and discrete element method (DEM) shows that the predicted particle concentration fields agree closely with reference solutions, with relative errors below 6%. The proposed approach reduces computational time by 71.4% and 95.5% compared to DEM for 1,000,000 particles and FEM simulations for 100,000 particles, respectively. Using the accelerated framework, systematic parametric studies are conducted over sound pressure level (SPL), excitation frequency, particle density and diameter. The results reinforce that particle transport and aggregation are governed by the coupling between acoustic forcing, flow field and particle inertia, leading to frequency- and density-dependent attenuation of particle displacement. This coupling also enhances collision probability for particles with larger size disparity and increased SPL. This work demonstrated FF-PINN to be an efficient approach for AA simulation that significantly reduces computational cost while maintaining adequate prediction accuracy.
