Related papers: A positivity-preserving adaptive-order finite-diff…
High-order finite volume and finite element methods offer impressive accuracy and cost efficiency when solving hyperbolic conservation laws with smooth solutions. However, if the solution contains discontinuities, these high-order methods…
We describe a newly developed hydrodynamic code for studying accretion disk processes. The numerical method uses a finite volume, nonlinear, Total Variation Diminishing (TVD) scheme to capture shocks and control spurious oscillations. It is…
We present a well-balanced finite volume solver for the compressible Euler equations with gravity where the approximate Riemann solver is derived using a relaxation approach. Besides the well-balanced property, the scheme is robust with…
Modern astrophysical simulations aim to accurately model an ever-growing array of physical processes, including the interaction of fluids with magnetic fields, under increasingly stringent performance and scalability requirements driven by…
In this paper, we present a multi-dimensional, arbitrary-order hybrid reconstruction framework for compressible flows on unstructured meshes. The method combines the efficiency of linear reconstruction with the robustness of high-order…
In this paper, we develop parametrized positivity satisfying flux limiters for the high order finite difference Runge-Kutta weighted essentially non-oscillatory (WENO) scheme solving compressible Euler equations to maintain positive density…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
In this paper we present a random shuffling scheme to apply with adaptive sorting algorithms. Adaptive sorting algorithms utilize the presortedness present in a given sequence. We have probabilistically increased the amount of presortedness…
We present a high order scheme for approximating kinetic equations with stiff relaxation. The objective is to provide efficient methods for solving the underlying system of conservation laws. The construction is based on several…
The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the…
We develop and analyze a class of maximum bound preserving schemes for approximately solving Allen--Cahn equations. We apply a $k$th-order single-step scheme in time (where the nonlinear term is linearized by multi-step extrapolation), and…
This study presents a novel, continuous finite-time control strategy for a class of nonlinear systems subject to matched uncertainties with unknown bounds. We propose an Adaptive Disturbance Observer-based Full-order Integral-Terminal…
We address the stabilization of linear, time-varying parabolic PDEs using finite-dimensional receding horizon controls (RHCs) derived from reduced-order models (ROMs). We first prove exponential stability and suboptimality of the…
This paper presents entropy symmetrization and high-order accurate entropy stable schemes for the relativistic magnetohydrodynamic (RMHD) equations. It is shown that the conservative RMHD equations are not symmetrizable and do not admit a…
This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the p-Laplacian, an optimal design problem in topology…
This work presents a method to adaptively refine reduced-order models \emph{a posteriori} without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive $h$-refinement: it enriches the reduced-basis space…
We design a conservative finite difference scheme for ideal magnetohydrodynamic simulations that attains high-order accuracy, shock-capturing, and divergence-free condition of the magnetic field. The scheme interpolates pointwise physical…
A long-standing and formidable challenge faced by all conservative schemes for relativistic magnetohydrodynamics (RMHD) is the recovery of primitive variables from conservative ones. This process involves solving highly nonlinear equations…
We present for astrophysical use a multi-dimensional numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference method on an Eulerian grid, called the Total Variation Diminishing…
This paper investigates the non-resistive compressible magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. We establish the global existence and stability of classical solutions for initial data sufficiently close to a constant…