Related papers: Compact Approximate Taylor methods for systems of …
We present an alternative pathway in the application of the variation improvement of ordinary perturbation theory exposed in [1] which can preserve the internal symmetries of a model by means of a time compactification.
We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and…
The high-order Target ENO (TENO) scheme, known for its innovative weighting strategy, has demonstrated strong potential for complex flow predictions. This study extends the TENO weighting approach to develop non-oscillatory central TENO…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
In this paper, we present a high order conservative semi-Lagrangian (SL) Hermite weighted essentially non-oscillatory (HWENO) method for the Vlasov equation based on dimensional splitting [Cheng and Knorr, Journal of Computational Physics,…
A new class of Hermite methods for solving nonlinear conservation laws is presented. While preserving the high order spatial accuracy for smooth solutions in the existing Hermite methods, the new methods come with better stability…
We study the famous example of weakly first order phase transitions in the 1+1D quantum Q-state Potts model at Q>4. We numerically show that these weakly first order transitions have approximately conformal invariance. Specifically, we find…
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
A novel central weighted essentially non-oscillatory (central WENO; CWENO)-type scheme for the construction of high-resolution approximations to discontinuous solutions to hyperbolic systems of conservation laws is presented. This procedure…
We present reliable a posteriori estimators for some fully discrete schemes applied to nonlinear systems of hyperbolic conservation laws in one space dimension with strictly convex entropy. The schemes are based on a method of lines…
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…
Conservative symmetric second-order one-step integrators are derived using the Discrete Multiplier Method for a family of vortex-blob models approximating the incompressible Euler's equations on the plane. Conservative properties and second…
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…
In this paper, we present convergence theorems for numerical solutions of the incompressible Euler equations. The first result is the Lax-Wendroff-type theorem, while the second can be formulated in the framework of the Lax equivalence…
In the Part 1 of the present paper the performance of several different low and high-order finite-volume methods were assessed by investigating how well they can capture the turbulent spectra of a compressible flow where small smooth…
A new type of finite volume WENO schemes for hyperbolic problems was devised in [36] by introducing the order-preserving (OP) criterion. In this continuing work, we extend the OP criterion to the WENO-Z-type schemes. We firstly rewrite the…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
A semi-implicit Lax-Wendroff kinetic scheme is developed for hydrodynamic phonon transport in solid materials based on the Boltzmann transport equation under the double relaxation time approximation, in which both the normal and resistive…
Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of…