Related papers: Shock Capturing by Bernstein Polynomials for Scala…
A new procedure to capture the shocks has been proposed and is demonstrated for the solutions of two-dimensional Euler equations using discontinuous Galerkin method and overset grids. A discontinuous Galerkin solver using a coarse grid…
The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for $n\times n$ hyperbolic conservation laws in one space dimension. These estimates are achieved by a "post-processing algorithm", checking that…
We are interested in the numerical approximation of discontinuous solutions in non conservative hyperbolic systems. An extension to second-order of a new strategy based on in-cell discontinuous reconstructions to deal with this challenging…
The compact scheme has high order accuracy and high resolution, but cannot be used to capture the shock. WENO is a great scheme for shock capturing, but is too dissipative for turbulence and small length scales. We developed a modified…
High-fidelity numerical simulation serves as a cornerstone for exploring magnetization dynamics in micromagnetics. This work introduces a novel third-order temporally accurate and stable numerical scheme for the Landau-Lifshitz-Gilbert…
We introduce a novel positivity-preserving, parameter-free numerical stabilisation approach for high-order discontinuous spectral element approximations of compressible multi-species flows. The underlying stabilisation method is the…
We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically…
We study compactness properties of time-discrete and continuous time BGK-type schemes for scalar conservation laws, in which microscopic interactions occur only when the state of a system deviates significantly from an equilibrium…
High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations.…
An approach for quantitatively evaluating overshooting oscillations is designed to characterize the performance of shock-capturing schemes. Specifically, following our previous work focused on cases with only discontinuities, now we account…
The recent theory of $a-$contraction with shifts provides $L^2$-stability for shock waves of $1-$D hyperbolic systems of conservation laws. The theory has been established at the inviscid level uniformly in the shock amplitude, and at the…
Modified versions of the Schr\"{o}dinger equation have been proposed in order to incorporate the description of measurement processes into the mathematical structure of quantum theory. Typically, these proposals introduce new physical…
We propose a change of variable approach and discontinuity capturing methods to ensure physical constraints for advection-reaction equations discretized by the finite element method. This change of variable confines the concentration below…
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order…
We equip a high-order continuous Galerkin discretization of a general hyperbolic problem with a nonlinear stabilization term and introduce a new methodology for enforcing preservation of invariant domains. The amount of shock-capturing…
Structure-preserving discretization of the Rosenbluth-Fokker-Planck equation is still an open question especially for unlike-particle collision. In this paper, a mass-energy-conserving isotropic Rosenbluth-Fokker-Planck scheme is…
Higher-order spectra (Brillinger's polyspectra) offer powerful methods for solving critical problems in signal processing and data analysis. Despite their significant potential, their practical use has remained limited due to unresolved…
The HLLEM scheme is a popular contact and shear preserving approximate Riemann solver for cheap and accurate computation of high speed gasdynamical flows. Unfortunately this scheme is known to be plagued by various forms of numerical shock…
The rotation-two-component Camassa--Holm system, which possesses strongly nonlinear coupled terms and high-order differential terms, tends to have continuous nonsmooth solitary wave solutions, such as peakons, stumpons, composite waves and…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…