相关论文: Enhancing stability of correction procedure via re…
A recently introduced framework of semidiscretisations for hyperbolic conservation laws known as correction procedure via reconstruction (CPR, also known as flux reconstruction) is considered in the extended setting of summation-by-parts…
The correction procedure via reconstruction (CPR, formerly known as flux reconstruction) is a framework of high order methods for conservation laws, unifying some discontinuous Galerkin, spectral difference and spectral volume methods.…
A generalised analytical notion of summation-by-parts (SBP) methods is proposed, extending the concept of SBP operators in the correction procedure via reconstruction (CPR), a framework of high-order methods for conservation laws. For the…
Stability is an important aspect of numerical methods for hyperbolic conservation laws and has received much interest. However, continuity in time is often assumed and only semidiscrete stability is studied. Thus, it is interesting to…
A fully implicit high-order preconditioned flux reconstruction/correction procedure via reconstruction (FR/CPR) method is developed to solve the compressible Navier-Stokes equations at low Mach numbers. A dual-time stepping approach with…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
We study the long-time error behavior of correction procedure via reconstruction / flux reconstruction (CPR/FR) methods for linear hyperbolic conservation laws. We show that not only the choice of the numerical flux (upwind or central)…
We present a filter stabilization technique for the mildly compressible Euler equations that relies on a linear or nonlinear indicator function to identify the regions of the domain where artificial viscosity is needed and determine its…
In the case of hyperbolic conservation laws, high-order methods, such as the classical DG method, experience the phenomenon of unwanted high-frequency oscillations in the vicinity of a shock. Shock-capturing methods such as artificial…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tensor-product framework. The dissipation operators can be…
High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summation-by-parts (SBP) operators and the weak enforcement of…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
The paper focuses on the development of numerical methods for the compressible Euler equations. It is well-known that if the Mach number is small, the system becomes stiff and hence explicit schemes suffer from severe time-step…
In this paper, we establish an initial theory regarding the Second Order Asymptotical Regularization (SOAR) method for the stable approximate solution of ill-posed linear operator equations in Hilbert spaces, which are models for linear…
For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach to construct entropy conservative/ dissipative…
We develop a $ P $-multigrid solver to simulate locally preconditioned unsteady compressible Navier-Stokes equations at low Mach numbers with implicit high-order methods. Specifically, the high-order flux reconstruction/correction procedure…
Entropy stable discontinuous Galerkin (DG) methods improve the robustness of high order DG simulations of nonlinear conservation laws. These methods yield a semi-discrete entropy inequality, and rely on an algebraic flux differencing…
We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit…
In this paper, we introduce a novel approach that combines multiresolution (MR) techniques with the flux reconstruction (FR) method to accurately and effciently simulate compressible flows. We achieve further enhancements in effciency…