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The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure, the spatial part of the dimensionless four-velocity and the particle density. Radially symmetric solutions of these equations are studied in two and ...

• A novel scheme is presented, able to efficiently compute solutions to the ultra-relativistic Euler equations in multi-d.
• For self-similar problems the one-dimensional scheme is compared to the solution of a corresponding ODE system.

This research focuses on exploring the regional controllability of position and fractional velocity within internally controlled hyperbolic systems. To achieve this, we leverage the Hilbert Uniqueness Method (HUM), which enables us to identify a ...$$$\mathrm{}$$\mathrm{}$

This paper studies the state estimation problem for a class of coupled linear ODE–hyperbolic PDE systems with unknown in-domain parameters. Based on the swapping transformation and the least squares parameter estimation method, a Luenberger-type ...

In this work we design and analyze an alternative to the Absorbing Boundary Conditions (ABC) or Perfectly Matched Layers (PML) technique to solve symmetric first order hyperbolic systems in unbounded domains. We propose a general formulation of ...

• A general Penalty Sponge Layer (PSL) for first order symmetric hyperbolic systems is proposed as an alternative of Perfectly Matched Layers (PML).
• Although the model is not PML, the penalty term acts quite effectively as shown by the ...

The paper focuses on first-order invariant-domain preserving approximations of hyperbolic systems. We propose a new way to estimate the artificial viscosity that has to be added to make explicit, conservative, consistent numerical methods ...

This paper primarily concerns the discontinuities capturing problems in nonconservative and nonconvex conservative hyperbolic systems. For the Godunov scheme of nonconservative hyperbolic systems, the numerical dissipation at discontinuous points ...

• Development of a novel point-wise based reconstruction for High Order Finite Volume scheme well suited AMR framework.

In this paper, a novel Finite Volume (FV) scheme for obtaining high order approximations of solutions of multi-dimensional hyperbolic systems of conservation laws within an Adaptive Mesh Refinement framework is proposed. It is based on ...

In this work, we present a modification of explicit Runge–Kutta temporal integration schemes that guarantees the preservation of any locally-defined quasiconvex set of bounds for the solution. These schemes operate on the basis of a bijective ...

• Characterization of first integral associated with approximate partial Hamiltonian operators.

We investigate a hyperbolic system that describe the dispersal dynamics of a population, introduced by Méndez and Camacho (1997)[1], in Lie symmetry classification perspective. A Lie group classification is provided for different forms ...

This paper considers general heterodirectional linear hyperbolic PDEs with boundary actuation and collocated measurement, that are bidirectionally coupled with nonlinear ODEs at the unactuated boundary. An output feedback regulator is ...

• Parameter-free approach for shock capturing in spectral element methods.
• ...

In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum ...

Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of mild ...

This paper deals with a class of efficient, genuinely two-dimensional Riemann solvers for hyperbolic nonconservative systems. A particularity of these solvers is that only a bound on the maximal propagation speeds in the coordinate directions is ...$$

In this paper, we investigate hyperbolic systems with random inputs based on generalized polynomial chaos (gPC) approximations, which is one of the most popular methods for uncertainty quantification (UQ) and can be implemented with either the ...

We design a leak detection, size estimation and localization algorithm for a branched pipe system, requiring flow and pressure measurements to be taken at the inlet and outlet boundaries, only. By showing that the pipe system model can ...

This paper is concerned with the fault diagnosis problem for general linear heterodirectional hyperbolic ODE–PDE systems. A systematic solution is presented for additive time-varying actuator, process and sensor faults in the presence ...

This paper deals with the development of efficient incomplete multidimensional Riemann solvers for hyperbolic systems. Departing from a four-waves model for the speeds of propagation arising at each vertex of the computational ...

• We propose a second-order genuinely two-dimensional class of incomplete Riemann solvers.

This paper studies the asymptotic behavior of switched linear systems, beyond classical stability. We focus on systems having a low-dimensional asymptotic behavior, that is, systems whose trajectories converge to a common time-varying ...

A new method is developed to approximate a first-order Hamilton–Jacobi equation. The constant motion of an interface in the normal direction is of interest. The interface is captured with the help of a “Level-Set” function approximated through a ...

In this paper, based on the continuous collocation polynomial approximations, we derive and analyse a class of trigonometric collocation integrators for solving the highly oscillatory hyperbolic system. The symmetry, convergence and energy ...