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The Lax-Friedrichs method in one-dimensional hemodynamics

The discretization of reduced one-dimensional hyperbolic models of blood flow using the Lax-Friedrichs method is discussed. Employing the well-established central scheme in this domain significantly simplifies the implementation of specific boundary …

A relaxation approach to the coupling of a two-phase fluid with a linear-elastic solid

A recently introduced coupling strategy for two nonconservative hyperbolic systems is employed to investigate a collapsing vapor bubble embedded in a liquid near a solid. For this purpose, an elastic solid modeled by a linear system of conservation …

A one-dimensional model for aspiration therapy in blood vessels

Aspiration thrombectomy is a treatment option for ischemic stroke due to occlusions in large vessels. During the therapy a device is inserted into the vessel and suction is applied. A new one-dimensional model is introduced that is capable of …

Error Estimates for First- and Second-Order Lagrange-Galerkin Moving Mesh Schemes for the One-Dimensional Convection-Diffusion Equation

A new moving mesh scheme based on the Lagrange-Galerkin method for the approximation of the one-dimensional convection-diffusion equation is studied. The mesh movement, which is prescribed by a discretized dynamical system for the nodal points, …

Numerical schemes for coupled systems of nonconservative hyperbolic equations

A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its stability …

A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model

We study a finite volume scheme approximating a parabolic-elliptic Keller-Segel system with power law diffusion with exponent γ∈[1,3] and periodic boundary conditions. We derive conditional a posteriori bounds for the error measured in the …

A data-driven microscopic on-ramp model based on macroscopic network flows

While macroscopic traffic flow models adopt a fluid dynamic description of traffic, microscopic traffic flow models describe the dynamics of individual vehicles. Capturing macroscopic traffic phenomena accurately remains a challenge for microscopic …

A central scheme for two coupled hyperbolic systems

A novel numerical scheme to solve coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the Lax curves of the coupled systems, which simplifies the computation of …

Data-Driven Models for Traffic Flow at Junctions

Traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based on car trajectory data we …

Central schemes for networked scalar conservation laws

We propose a novel scheme to numerically solve scalar conservation laws on networks without the necessity to solve Riemann problems at the junction. The scheme is derived using the relaxation system introduced in [Jin and Xin, Comm. Pure Appl. Math. …