An h-Adaptive RKDG Method for the Vlasov–Poisson System

Abstract

In this paper, we propose a new h-adaptive indicator for the Runge-Kutta discontinuous Galerkin (RKDG) scheme in simulations of the Vlasov-Poisson (VP) system. This adaptive indicator, tailored for the VP system, is based on the principle that each cell assumes solution variations as equally as possible. Under the framework of the RKDG method, such adaptive indicator is particularly simple and cheap for the computation. Its effectiveness is demonstrated by extensive numerical tests. The detailed adaptive algorithm as well as some important implementation issues, including the grid and data structure, adaptive criteria, data prolongation/projection and mesh projection, is presented.

Comparison of Semi-Lagrangian Discontinuous Galerkin Schemes for Linear and Nonlinear Transport Simulations

“…Consider the strong Landau damping for the VP system with the initial condition being a perturbed Maxwellian equilibrium where = 0.5 and k 0 = 0.5 . This problem has been numerically investigated by several authors, e.g., see [15,32,44,51,60]. First, we perform the comparison for Q k SLDG-split and P k SLDG-(QC)-time(k + 1) , k = 1, 2 .…”

Efficient degradation of organic pollutants by peroxymonosulfate activated with MgCuFe-layered double hydroxide

“…A constant pH co-precipitation method was used to synthesize MgCuFe-LDH. 27 Briey, a solution containing Mg(NO 3 ) 2 $6H 2 O (48 mmol), Cu(NO 3 ) 2 $3H 2 O (12 mmol) and Fe(NO 3 ) 3 $9H 2 O (20 mmol) was prepared in 100 mL ultrapure water. Another solution was made by dissolving NaOH (1 mol L À1 ) and Na 2 CO 3 (2 mol L À1 ) in ultrapure water.…”

“…The (003) spacing of MgCuFe-LDH, MgCuAl-LDH, and MgFe-LDH were calculated to be $0.770, $0.767 and $0.773 nm, respectively, which are consistent with the value of LDH with carbonate intercalation reported in previous studies. 27,28 The FTIR spectra of MgCuFe-LDH, MgCuAl-LDH and MgFe-LDH ( Fig. 2b) adsorption-desorption isotherm curves of samples exhibit a type IV isotherm with H3-type hysteresis loop in the IUPAC classication.…”

A High Order Conservative Semi-Lagrangian Discontinuous Galerkin Method for Two-Dimensional Transport Simulations

“…This problem has been numerically investigated by several authors, e.g. see [41,14,49,57,29]. First, we perform the comparison for Q k SLDG-split and P k SLDG-(QC)-timek + 1, k = 1, 2.…”