Youngsoo Ha

An improved weighted essentially non-oscillatory scheme with a new smoothness indicator

In this paper, we present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions, especially at critical points where the first derivative vanishes (but the second derivatives are non-zero). We provide a detailed analysis to verify the fifth-order accuracy. Some numerical experiments are presented to demonstrate the performance of the proposed scheme. We see that the proposed WENO scheme provides at least the same or improved behavior over the fifth-order WENO-JS scheme [10] and other fifth-order WENO schemes called as WENO-M [9] and WENO-Z [2], but its advantage seems more salient in two dimensional problems.

Numerical Simulation of High Mach Number Astrophysical Jets with Radiative Cooling

Computational fluid dynamics simulations using the WENO-LF method are applied to high Mach number nonrelativistic astrophysical jets, including the effects of radiative cooling. Our numerical methods have allowed us to simulate astrophysical jets at much higher Mach numbers than have been attained (Mach 20) in the literature. Our simulations of the HH 1-2 astrophysical jets are at Mach 80. Simulations at high Mach numbers and with radiative cooling are essential for achieving detailed agreement with the astrophysical images.

On the numerical solution of a driven thin film equation

This paper is devoted to comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is u t + ( u 2 - u 3 ) x = - ( u 3 u xxx ) x , which arises in the context of thin film flow. First we employ implicit schemes and treat both convection and diffusion terms implicitly. Then the convection terms are treated with well-known explicit schemes, namely Godunov, WENO and an upwind-type scheme, while the diffusion term is still treated implicitly. The diffusion and convection schemes are combined using a fractional step-splitting method.

Modified Non-linear Weights for Fifth-Order Weighted Essentially Non-oscillatory Schemes

This paper is concerned with fifth-order weighted essentially non-oscillatory (WENO) scheme with a new smoothness indicator. As the so-called WENO-JS scheme (Jiang and Shu in J Comput Phys 126:202–228, 1996) provides the third-order accuracy at critical points where the first and third order derivatives do not becomes zero simultaneously, several fifth-order WENO scheme have been developed through modifying the known smoothness indicators of WENO-JS. Recently a smoothness indicator based on

Modified Essentially Nonoscillatory Schemes Based on Exponential Polynomial Interpolation for Hyperbolic Conservation Laws

L^1

Sixth-order Weighted Essentially Nonoscillatory Schemes Based on Exponential Polynomials

L1-norm has been proposed by Ha et al. (J Comput Phys 232:68–86, 2013) (denoted by WENO-NS). The aim of this paper is twofold. Firstly, we further improve the smoothness indicator of WENO-NS and secondly, using this measurement, we suggest new nonlinear weights by simplifying WENO-NS weights. The proposed WENO scheme provides the fifth-order accuracy, even at critical points. Some numerical experiments are provided to demonstrate that the present scheme performs better than other WENO schemes of the same order.

A variational approach to blending based on warping for non-overlapped images

Abstract High Mach number astrophysical jets are simulated using a positive scheme, and are compared with WENO-LF simulations. A version of the positive scheme has allowed us to simulate astrophysical jets with radiative cooling up to Mach number 270 with respect to the heavy jet gas, a factor of two times higher than the maximum Mach number attained with the WENO schemes and ten times higher than with CLAWPACK. Such high Mach numbers occur in many settings in astrophysical flows, so it is important to develop a scheme that can simulate at these Mach numbers.

Hybrid Finite Difference Weighted Essentially Non-oscillatory Schemes for the Compressible Ideal Magnetohydrodynamics Equation

This study proposes modified essentially nonoscillatory (ENO) schemes that can improve the performance of the classical ENO schemes. The key ideas of our approach consist of the following two approaches. First, the interpolation method is implemented by using exponential polynomials with shape (or tension) parameters such that they can be tuned to the characteristics of given data, yielding better approximation than the classical ENO schemes at the same computational cost. Second, we present a new smoothness measurement that can evaluate the local smoothness of a function inside a stencil such that it enables the identification of the smoothest one, while avoiding the inclusion of discontinuous points in the stencil. Some numerical experiments are provided to demonstrate the performance of the proposed schemes.