Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2108.08820

A new two-dimensional blood flow model with arbitrary cross sections

Cesar Alberto Rosales-Alcantar·Gerardo Hernandez-Duenas
View original source ↗Read source document ↗Export metadata ↓

Abstract

A new two-dimensional model for blood flows in arteries with arbitrary cross sections is derived. The model consists of a system of balance laws for conservation of mass and balance of momentum in the axial and angular directions. The equations are derived by applying asymptotic analysis to the incompressible Navier-Stokes equations in narrow, large vessels and integrating in the radial direction in each cross section. The main properties of the system are discussed and a positivity-preserving well-balanced central-upwind scheme is presented. The merits of the scheme will be tested in a variety of scenarios. In particular, numerical results of simulations using an idealized aorta model are shown. We analyze the time evolution of the blood flow under different initial conditions such as perturbations to steady states consisting of a bulging in the vessel's wall. We consider different situations given by distinct variations in the vessel's elasticity.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Cesar Alberto Rosales-Alcantar, Gerardo Hernandez-Duenas. 2021-08-20. A new two-dimensional blood flow model with arbitrary cross sections. https://arxiv.org/abs/2108.08820

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

$L^{p}$-convergence of Kantorovich-type Max-Min Neural Network Operators

In this work, we study the Kantorovich variant of max-min neural network operators, in which the operator kernel is defined in terms of sigmoidal functions. Our main aim is to demonstrate the $L^{p}$-convergence of these nonlinear operators for $1\leq p<\infty$, which makes it possible to obtain approximation results for functions that are not necessarily continuous. In addition, we will derive quantitative estimates for the rate of approximation in the $L^{p}$-norm. We will provide some explicit examples, studying the approximation of discontinuous functions with the max-min operator, and varying additionally the underlying sigmoidal function of the kernel. Further, we numerically compare the $L^{p}$-approximation error with the respective error of the Kantorovich variants of other popular neural network operators. As a final application, we show that the Kantorovich variant has advantages compared to the sampling variant of the max-min operator and Kantorovich variant of the max-product operator when it comes to approximate noisy functions as for instance biomedical ECG signals.

math.NA↗
arXiv2026

Quotient geometry of tensor ring decomposition

Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its intrinsic geometry remains less understood, primarily due to the underlying ring structure and the resulting nontrivial gauge invariance. We establish the quotient geometry and immersed-submanifold structure of TR decomposition by imposing full-rank conditions on all unfolding matrices of the core tensors and capturing the gauge invariance. The intrinsic ring structure of TR leads to an analysis that is substantially different from other tensor formats. Additionally, for the uniform TR decomposition, where all core tensors are identical and the manifold structure is known, we derive explicit parameterizations for the vertical and horizontal spaces, which enable Riemannian optimization. Numerical experiments validate the developed geometries via tensor ring completion tasks.

math.NA↗
arXiv2026

Boundary elements for clamped Kirchhoff--Love plates

We present a Galerkin boundary element method for clamped Kirchhoff--Love plates with piecewise smooth boundary. It is a direct method based on the representation formula and requires the inversion of the single-layer operator, an application of the double-layer operator to the Dirichlet data, and, in the presence of a vertical load, an application of the Dirichlet trace of the Newton potential to that load. We present trace approximation spaces of arbitrary order, required for both the Dirichlet data and the unknown Neumann trace. Our boundary element method is quasi-optimal with respect to the natural trace norm and achieves optimal convergence order under minimal regularity assumptions. We provide explicit representations of all three integral operators and discuss the implementation of the appearing integrals. Numerical experiments for smooth and non-smooth domains confirm predicted convergence rates.

math.NA↗