We have developed a new monotone cell-centered finite volume method for the discretization of diffusion equations on conformal polyhedral meshes. The proposed method is based on a nonlinear two-point flux approximation. For problems with smooth diffusion tensors and Dirichlet boundary conditions the method is interpolation-free. An adaptive interpolation is applied on faces where diffusion tensor jumps or Neumann boundary conditions are imposed. The interpolation is based on physical relationships such as continuity of the diffusion flux. The second-order convergence rate is verified with numerical experiments.

This work is the numerical study of the age-dependent responses of the vascular system under low-mass high-speed impact scenario. The grid-characteristic method on the adaptive mesh model of the human thorax is the numerical tool of the study. Due to the lack of valid vascular injury criteria, the numerical model only provides information on injury risk. The numerical simulation demonstrates that an older age changes significantly the vascular response and increases the risk of aorta injury. We focused on the aorta because its rupture is the general consequence of vehicle accidents (great mass impacts at relatively low velocity). Our numerical results are in good agreement with previous studies of great-mass low-speed blunt thorax impact.

This paper proposes a quantitative model of the reaction-diffusion type to examine the distribution of interferon-α (IFNα) in a lymph node (LN). The numerical treatment of the model is based on using an original unstructured mesh generation software Ani3D and nonlinear finite volume method for diffusion equations. The study results in suggestion that due to the variations in hydraulic conductivity of various zones of the secondary lymphoid organs the spatial stationary distribution of IFNα is essentially heterogeneous across the organs. Highly protected domains such as sinuses, conduits, co-exist with the regions in which where the stationary concentration of IFNα is lower by about 100-fold. This is the first study where the spatial distribution of soluble immune factors in secondary lymphoid organs is modelled for a realistic three-dimensional geometry.

We present a robust unstructured tetrahedral mesh generation technology. This technology is a combination of boundary discretization methods, an advancing front technique and a Delaunay-based mesh...

This study introduces an innovative approach leveraging physics-informed neural networks (PINNs) for the efficient computation of blood flows at the boundaries of a four-vessel junction formed by a Fontan procedure. The methodology incorporates a 3D mesh generation technique based on the parameterization of the junction’s geometry, coupled with an advanced physically regularized neural network architecture. Synthetic datasets are generated through stationary 3D Navier–Stokes simulations within immobile boundaries, offering a precise alternative to resource-intensive computations. A comparative analysis of standard grid sampling and Latin hypercube sampling data generation methods is conducted, resulting in datasets comprising $1.1\times {10}^4$ and $5\times {10}^3$ samples, respectively. The following two families of feed-forward neural networks (FFNNs) are then compared: the conventional “black-box” approach using mean squared error (MSE) and a physically informed FFNN employing a physically regularized loss function (PRLF), incorporating mass conservation law. The study demonstrates that combining PRLF with Latin hypercube sampling enables the rapid minimization of relative error (RE) when using a smaller dataset, achieving a relative error value of $6\%$ on the test set. This approach offers a viable alternative to resource-intensive simulations, showcasing potential applications in patient-specific 1D network models of hemodynamics.