arXiv subjects

Satoshi Ii

Publications and source records attributed to Satoshi Ii.

9 recordsLinked to original sources

arXiv2026

Reconstruction of instantaneous flow fields from transient velocity snapshots using physics-informed neural networks: Applications to pulsatile blood flow behind a stenosis

Physics-informed neural networks (PINNs) offer a promising framework by embedding partial differential equations (PDEs) into the loss function together with measurement data, making them well-suited for inverse problems. However, standard PINNs face challenges with time-dependent PDEs due to the high computational cost of space-time training and the risk of convergence to local minima. These limitations are particularly pronounced in hemodynamic analysis, where 4D-flow magnetic resonance imaging (4D-flow MRI) yields temporally sparse velocity snapshots over the cardiac cycle. To address this challenge, we propose a PINN framework that reconstructs instantaneous flow fields from transient velocity snapshots by inferring the acceleration term in the incompressible Navier-Stokes equations. By designing the network without explicit time as an input, the proposed approach enables physics enforcement using spatial evaluations alone, improving training efficiency while maintaining physical consistency with transient flow characteristics. In addition, we introduce an acceleration-mismatch loss that penalizes discrepancies between predicted and measured accelerations, which improves prediction accuracy through regularization. Numerical examples on pulsatile flow behind a stenosis using temporally and spatially downsampled synthetic data generated from time-resolved CFD demonstrate that the proposed framework reliably reconstructs velocity fields even under sparse temporal sampling, and appropriate regularization for acceleration improves predictions of pressure-gradient and acceleration fields.

physics.flu-dyn↗

arXiv2025

A pressure-projection formulation in a least-squares meshfree method for the incompressible Navier-Stokes equations using a staggered-variable arrangement

Incompressible flow solvers based on strong-form meshfree methods represent arbitrary geometries without the need for a global mesh system. However, their local evaluations make it difficult to satisfy incompressibility at the discrete level. Moreover, the collocated arrangement of velocity and pressure variables tends to induce a zero-energy mode, leading to decoupling between the two variables. In projection-based approaches, a spatial discretization scheme based on a conventional node-based moving least-squares method for the pressure causes inconsistency between the discrete operators on both sides of the Poisson equation. Thus, a solenoidal velocity field cannot be ensured numerically. In this study, a numerical method for the incompressible Navier-Stokes equations is developed by introducing a local primal-dual grid into the mesh-constrained discrete point method, enabling consistent discrete operators. The constructed virtual dual cell is defined solely from the local connectivity among nodes, and thus the method retains its meshfree nature. To achieve a consistent coupling between velocity and pressure variables under the primal-dual arrangement, time evolution converting is applied to evolve the velocity on cell interfaces. For numerical validation, a linear acoustic equation is solved to confirm the effectiveness of the staggered-variable arrangement based on the local primal-dual grid. Then, incompressible Navier-Stokes equations are solved, and the proposed method is demonstrated to ensure a local divergence-free velocity field up to an arbitrarily small discrete error, achieve the expected spatial convergence order, and accurately reproduce flow features over a wide range of Reynolds numbers.

math.NA↗

arXiv2025

Diffuse interface approach to oxygen transport and metabolism under blood flow dynamics in microcirculations

The relationship between the spatiotemporal distribution of oxygen transport and blood flow dynamics, accounting for the motion and deformation of individual red blood cells (RBCs), is of fundamental importance for understanding microcirculation systems. Three-dimensional (3D) modeling is indispensable for addressing complex oxygen transport and cellular behaviors in capillary networks; however, the computational approach is formidable for enforcing interface (or jump) conditions on largely moving and deforming interfaces. In this paper, we propose a diffuse interface approach for the oxygen transport using a mixture formulation. We formulate oxygen transport using an advection-diffusion-reaction equation and rewrite all governing equations in mixture forms using phase indicator functions, where all the interface conditions are included in the governing equations. This innovation avoids the complexity associated with discontinuities for largely moving interfaces in highly dense RBC conditions. We model cellular flow as a fluid-membrane interaction problem using the immersed boundary method (IBM). The method allows the seamless calculation of coupling problems for cellular flows and oxygen transports in the cytoplasm (internal fluid) of the RBC, plasma (external fluid), and tissue regions using a fixed Cartesian coordinate mesh. The proposed method accurately captures the analytical solution for spherically symmetric diffusion, and successfully demonstrates oxygen transport in both straight capillaries and their networks. These rigorous analyses suggest that RBCs can autonomously regulate the oxygen supply to tissues in response to the local tissue oxygenation level, resulting in the establishment of homogeneous tissue oxygenation.

physics.flu-dyn↗

arXiv2025

Fine-tuning physics-informed neural networks for cavity flows using coordinate transformation

Physics-informed neural networks (PINNs) have attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for many applications. Despite the versatility of PINNs, it remains challenging to reduce their training cost. Using a DNN pre-trained with an arbitrary dataset with transfer learning or fine-tuning is a potential solution. However, a pre-trained model using a different geometry and flow condition than the target may not produce suitable results. This paper proposes a fine-tuning approach for PINNs with coordinate transformation, modelling lid-driven cavity flows with various shapes. We formulate the inverse problem, where the reference data inside the domain and wall boundary conditions are given. A pre-trained PINN model with an arbitrary Reynolds number and shape is used to initialize a target DNN. To reconcile the reference shape with different targets, governing equations as a loss of the PINNs are given with coordinate transformation using a deformation gradient tensor. Numerical examples for various cavity flows with square, rectangular, shear deformed and inflated geometries demonstrate that the proposed fine-tuning approach improves the training convergence compared with a randomly-initialized model. A pre-trained model with a similar geometry to the target further increases training efficiency. These findings are useful for real-world applications such as modelling intra-aneurysmal blood flows in clinical use.

physics.flu-dyn↗

arXiv2024

A mesh-constrained discrete point method for incompressible flows with moving boundaries

Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which is enhanced over time and result in problems in computational efficiency and parallel computations. To mitigate these problems, a mesh-constrained discrete point (MCD) method was developed for stationary boundary problems (Matsuda et al., 2022). Although the MCD method is a meshless method that uses moving least-squares approximation, the arrangement of particles (or discrete points (DPs)) is specialized so that their positions are constrained in background meshes to obtain a closely uniform distribution. This achieves a reasonable approximation for spatial derivatives with compact stencils without encountering any ill-posed condition and leads to good performance in terms of computational efficiency. In this study, a novel meshless method based on the MCD method for incompressible flows with moving boundaries is proposed. To ensure the mesh constraint of each DP in moving boundary problems, a novel updating algorithm for the DP arrangement is developed so that the position of DPs is not only rearranged but the DPs are also reassigned the role of being on the boundary or not. The proposed method achieved reasonable results in numerical experiments for well-known moving boundary problems.

physics.flu-dyn↗

arXiv2022

A particle-based method using the mesh-constrained discrete point approach for two-dimensional Stokes flows

Meshless methods inherently do not require mesh topologies and are practically used for solving continuum equations. However, these methods generally tend to have a higher computational load than conventional mesh-based methods because calculation stencils for spatial discretization become large. In this study, a novel approach for the use of compact stencils in meshless methods is proposed, called the mesh-constrained discrete point (MCD) approach. The MCD approach introduces a Cartesian mesh system to the background of a domain. And the approach rigorously constrains the distribution of discrete points (DPs) in each mesh by solving a dynamic problem with nonlinear constraints. This can avoid the heterogeneity of the DP distribution at the mesh-size level and impose compact stencils with a fixed degree of freedom for derivative evaluations. A fundamental formulation for arrangements of DPs and an application to unsteady Stokes flows are presented in this paper. Numerical tests were performed for the distribution of DPs and flow problems in co-axial and eccentric circular channels. The proposed MCD approach achieved a reasonable distribution of DPs independently of the spatial resolution with a few iterations in pre-processing. Additionally, solutions using the obtained DP distributions in Stokes flow problems were in good agreement with theoretical and reference solutions. The results also confirmed that the numerical accuracies of velocity and pressure achieved the expected convergence order, even when compact stencils were used.

physics.flu-dyn↗

arXiv2012

CIP/multi-moment finite volume method with arbitrary order of accuracy

This paper presents a general formulation of the CIP/multi-moment finite volume method (CIP/MM FVM) for arbitrary order of accuracy. Reconstruction up to arbitrary order can be built on single cell by adding extra derivative moments at the cell boundary. The volume integrated average (VIA) is updated via a flux-form finite volume formulation, whereas the point-based derivative moments are computed as local derivative Riemann problems by either direct interpolation or approximate Riemann solvers.

physics.comp-ph↗

arXiv2012

A note on the general multi-moment constrained flux reconstruction formulation for high order schemes

This paper presents a general formulation to construct high order numerical schemes by using multi-moment constraint conditions on the flux function reconstruction. The new formulation, so called multi-moment constrained flux reconstruction (MMC-FR), distinguishes itself essentially from the flux reconstruction formulation (FR) of Huynh (2007) by imposing not only the continuity constraint conditions on the flux function at the cell boundary, but also other types constraints which may include those on the spatial derivatives or the point values. This formulation can be also interprated as a blend of Lagrange interpolation the Hermite interpolation, which provides a numerical framework to accomodate a wider spectrum of high order schemes. Some representative schemes will be presented and evaluated through Fourier analysis and numerical tests.

physics.comp-ph↗

arXiv2010

A full Eulerian finite difference approach for solving fluid-structure coupling problems

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.

physics.comp-ph↗