Related papers: Spectral shock detection for dynamically developin…
The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic…
Spectral methods yield numerical solutions of the Galerkin-truncated versions of nonlinear partial differential equations involved especially in fluid dynamics. In the presence of discontinuities, such as shocks, spectral approximations…
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…
In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce…
A main disadvantage of many high-order methods for hyperbolic conservation laws lies in the famous Gibbs-Wilbraham phenomenon, once discontinuities appear in the solution. Due to the Gibbs-Wilbraham phenomenon, the numerical approximation…
Generalized polynomial chaos (gPC) method has been extensively used in uncertainty quantification problems where equations contain random variables. For gPC to achieve high accuracy, PDE solutions need to have high regularity in the random…
This contribution Part II of a two-part series, extends the general-domain FC-SDNN (Fourier Continuation Shock-Detecting Neural Network) introduces in Part I to enable treatment of non-smooth domains, it introduces a parallel implementation…
The goal of this work is to develop a new universal high order subroutine for shock boundary layer interaction. First, an effective shock/discontinuity detector has been developed.The detector has two steps.The first step is to check the…
Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and $L_2$-norm.…
In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the…
Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g. the inviscid Burgers equation for the simple exclusion process. The physical solutions of…
Partial differential equations are frequently solved using a global basis, such as the Fourier series, due to excellent convergence. However, convergence becomes impaired when discontinuities are present due to the Gibbs phenomenon,…
In this paper, we present a new formulation of smoothed particle hydrodynamics (SPH), which, unlike the standard SPH (SSPH), is well-behaved at the contact discontinuity. The SSPH scheme cannot handle discontinuities in density (e.g. the…
We study a nonlocal Poisson problem with discontinuous source term and analyze how the regularity of the integral kernel determines the discontinuity structure of the corresponding solution. Under general assumptions on compactly supported…
This paper presents a spectral scheme for the numerical solution of nonlinear conservation laws in non-periodic domains under arbitrary boundary conditions. The approach relies on the use of the Fourier Continuation (FC) method for spectral…
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…
A new approach to prevent spurious behavior caused by conventional shock-capturing schemes when solving stiff detonation waves problems is introduced in the present work. Due to smearing of discontinuous solution by the excessive numerical…
A new combined sub-filter scale turbulence and shock-capturing model is developed for high-order finite volume numerics, extending previous work to unstructured solvers. Block Spectral Stresses (BSS) method relies on the spectra of the…
Solving compressible flows containing discontinuities remains a major challenge for numerical methods especially on unstructured grids. Thus in this work, we make contributions to shock capturing schemes on unstructured grids with aim of…
Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of the weak rod model of Blake and Zisserman (1987) that allows…