Related papers: Exact solutions and conservation lawsof a one-dime…
The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…
One-dimensional (1D) blood flow simulations are extensively used in cardiovascular research due to their computational efficiency and effectiveness in analyzing pulse wave dynamics. Despite their versatility and simplicity, there is a lack…
Understanding the physics of blood is challenging due to its nature as a suspension of soft particles and the fact that typical problems involve different scales. This is valid also for numerical investigations. In fact, many computational…
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…
In the last years, medical computer simulation has seen a great growth in several scientific branches, from modelling to numerical methods, going through computer science. The main goals of this incipient discipline are testing hypotheses…
Computational cardiovascular flow modeling plays a crucial role in understanding blood flow dynamics. While 3D models provide acute details, they are computationally expensive, especially with fluid-structure interaction (FSI) simulations.…
Mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand physiological and pathological processes. The theory behind the phenomenon is closely related…
The one-dimensional viscous conservation law is considered on the whole line $$ u_t + f(u)_x=\eps u_{xx},\quad (x,t)\in\RR\times\overline{\RP},\quad \eps>0, $$ subject to positive measure initial data. The flux $f\in C^1(\RR)$ is assumed to…
The nonlinear inviscid 1D blood flow equations are studied analytically using the method of characteristics. The boundary value problem with a triangle-shaped boundary data at the aortic outlet is considered. The pressure-velocity profile,…
The paper considers one-dimensional flows of polytropic (calorically ideal) gas. These flows include three cases of gas dynamics: plain one-dimensional flows (one-dimensional space), radially symmetric flows in two-dimensional space and…
We study the inflow-outflow boundary value problem on an interval, the analog of the 1D shock tube problem for gas dynamics, for general systems of hyperbolic-parabolic conservation laws. In a first set of investigations, we study…
We study dispersive models of fluid flow in viscoelastic vessels, derived in the study of blood flow. The unknowns in the models are the velocity of the fluid in the axial direction and the displacement of the vessel wall from rest. We…
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely…
Travelling waves and conservation laws are studied for a wide class of U(1)-invariant complex mKdV equations containing the two known integrable generalizations of the ordinary (real) mKdV equation. The main results on travelling waves…
We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
We consider a planar viscous shock for a scalar viscous conservation law with a strictly convex flux in multi-dimensional setting, where the transversal direction is periodic. We first show the contraction property for any solutions…
We study the behavior of the pulse waves of water into a flexible tube for application to blood flow simulations. In pulse waves both fluid friction and wall viscosity are damping factors, and difficult to evaluate separately. In this…
This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…
We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…