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 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 …
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 …
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, …
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 …
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 …
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 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 …
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 …
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. …