Monotonicity Preserving Interpolation Using Rational Quartic Said-Ball Function

2021 ◽  
pp. 565-574
Author(s):  
Samsul Ariffin Abdul Karim ◽  
Van Thien Nguyen
Keyword(s):  
Monotonicity Preserving

scholarly journals On nonpolynomial monotonicity‐preserving C 1 spline interpolation

2021 ◽  
Author(s):  
Domingo Barrera ◽  
Salah Eddargani ◽  
Abdellah Lamnii ◽  
Mohammed Oraiche
Keyword(s):  
Spline Interpolation ◽  
Monotonicity Preserving

scholarly journals Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Yuanpeng Zhu ◽  
Xuli Han ◽  
Shengjun Liu
Keyword(s):  
Error Estimate ◽  
Hermite Interpolation ◽  
Sufficient Conditions ◽  
Basis Functions ◽  
Shape Parameters ◽  
Interpolation Spline ◽  
Triangular Domain ◽  
Type Algorithm ◽  
Special Case ◽  
Monotonicity Preserving

Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class ofC1continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing aC1positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, theG1continuous conditions are deduced for the joining of two patches.

Transient Radiative Transfer in Anisotropically Scattering Media Using Monotonicity-Preserving Schemes

2000 ◽  
Author(s):  
M. Sakami ◽  
K. Mitra ◽  
P.-F. Hsu
Keyword(s):  
Radiative Transfer ◽  
Research Work ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Discrete Ordinates Method ◽  
Piecewise Parabolic ◽  
Phase Functions ◽  
Monotonicity Preserving ◽  
Made In ◽  
Thick Medium

Abstract This research work deals with the analysis of transient radiative transfer in one-dimensional scattering medium. The time-dependant discrete ordinates method was used with an upwind monotonic scheme: the piecewise parabolic scheme. This scheme was chosen over a total variation diminishing version of the Lax-Wendroff scheme. These schemes were originally developed to solve Eulerian advection problem in hydrodynamics. The capability of these schemes to handle sharp discontinuity in a propagating electromagnetic wave front was compared. The accuracy and the efficiency of the discrete ordinates method associated with the piecewise parabolic advection scheme were studied. Comparisons with Monte Carlo and integral formulation methods show the accuracy and the efficiency of this proposed method. Parametric study for optically thin and thick medium, different albedos and phase functions is then made in the unsteady state zone.

AUSM-Based High-Order Solution for Euler Equations

2012 ◽  
Vol 12 (4) ◽  
pp. 1096-1120 ◽  
Author(s):  
Angelo L. Scandaliato ◽  
Meng-Sing Liou
Keyword(s):  
Euler Equations ◽  
Splitting Method ◽  
High Order ◽  
Riemann Solvers ◽  
Carbuncle Phenomenon ◽  
Solution Accuracy ◽  
Matrix Vector ◽  
Approximate Riemann Solvers ◽  
Monotonicity Preserving ◽  
High Order Interpolation

AbstractIn this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method (AUSM), specifically AUSM+-UP, with high-order upwind-biased interpolation procedures, the weighted essentially non-oscillatory (WENO-JS) scheme and its variations, and the monotonicity preserving (MP) scheme, for solving the Euler equations. MP is found to be more effective than the three WENO variations studied. AUSM+-UP is also shown to be free of the so-called “carbuncle” phenomenon with the high-order interpolation. The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables, even though they require additional matrix-vector operations. Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison. In addition, four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy. Finally, a measure for quantifying the efficiency of obtaining high order solutions is proposed; the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.

scholarly journals Hybrid Flux Method in Monotonicity-Preserving Scheme for Accurate and Robust Simulation in Supersonic Flow

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Myeong-Hwan Ahn ◽  
Duck-Joo Lee
Keyword(s):  
Blow Up ◽  
Supersonic Jet ◽  
Positive Density ◽  
Computational Domain ◽  
Flux Method ◽  
Present Scheme ◽  
Local Extrema ◽  
Volume Method ◽  
Fifth Order ◽  
Monotonicity Preserving

The fifth-order monotonicity-preserving (MP5) scheme is an accurate and low dissipative numerical method. As a finite-volume method, MP5 adopts the Roe-flux scheme for solving the numerical flux in the compressible Euler equation. However, due to the deficiency of the MP limiter and Roe-flux in maintaining positive density and pressure, the calculation could fail in cases of extreme flow involving small values of density and pressure. In this study, to overcome such a limitation but still to achieve a high-accuracy of MP5, we propose a hybrid flux method: the Roe-flux is used in the global computational domain, but the first-order Lax-Friedrich (LF)-flux is adopted only for trouble grids. The numerical results of shock-tube and complicated interaction problems indicate that the present scheme is more accurate at discontinuities and local extrema compared to the previous scheme, maintaining positive density and pressure values. For two-dimensional applications, a supersonic jet is explored with different Mach numbers and temperature conditions. As a result, small vortices induced by the shear layer can be clearly captured by the proposed scheme. Furthermore, a simulation was successfully conducted without blow-up of calculation even in the extreme jet flow condition.

Sign in / Sign up

Export Citation Format

Share Document