Generalized Characteristic Interface Conditions with High-Order Interpolation Method

2008 ◽  
Author(s):  
Takahiro Sumi ◽  
Takuji Kurotaki ◽  
Jun Hiyama
Keyword(s):  
Interpolation Method ◽  
High Order ◽  
Interface Conditions ◽  
High Order Interpolation

High-Order Interpolation Method for Overset Grid Based on Finite Volume Method

AIAA Journal ◽  
2011 ◽  
Vol 49 (7) ◽  
pp. 1387-1398 ◽  
Author(s):  
Kyung Rock Lee ◽  
Jung Ho Park ◽  
Kyu Hong Kim
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Interpolation Method ◽  
High Order ◽  
Overset Grid ◽  
Volume Method ◽  
High Order Interpolation ◽  
Grid Based

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.

Convergence of a highly accurate quasi-interpolation method for options pricing

2017 ◽  
Vol 04 (04) ◽  
pp. 1750048
Author(s):  
Shengliang Zhang
Keyword(s):  
Stock Price ◽  
Interpolation Method ◽  
High Order ◽  
Basis Functions ◽  
High Order Accuracy ◽  
Options Pricing ◽  
Interpolation Scheme ◽  
Time Step ◽  
Order Accuracy ◽  
Tree Approach

A highly accurate radial basis functions (RBFs) quasi-interpolation method for calculating American options prices has been presented by some researchers, which possesses a high order accuracy compared with existing numerical methods. In this study, we show the convergence of the proposed RBFs quasi-interpolation scheme from the view point of probability. It will be confirmed to be a multinomial tree approach, in which in one time step the underlying stock price can arrive at an infinity of possible values. This helps understand the high-order accuracy of the method.

Assessment of Enhanced Multi-Dimensional Limiting Process for Multi-Dimensional Flows

2011 ◽  
Author(s):  
Kyu Hong Kim ◽  
Jung Ho Park
Keyword(s):  
Higher Order ◽  
High Order ◽  
Test Cases ◽  
Computational Domain ◽  
Interpolation Scheme ◽  
Local Extrema ◽  
Numerous Test ◽  
High Order Interpolation

In this paper, a new limiting process based on the Multi-dimensional Limiting Process, called enhanced Multi-dimensional Limiting Process is developed and tested with several cases. The enhanced Multi-dimensional Limiting Process, e-MLP has a number of useful features of MLP limiter such as multi-dimensional monotonicity and straightforward extensionality to higher order interpolation. It is applicable to local extrema and prevents excessive damping in a linear discontinuous region through application of appropriate limiting criteria. It is efficient because a limiting function is applied only to a discontinuous region. In addition, it is robust against shock instability due to the strict distinction of the computational domain and the use of regional information in a flux scheme as well as a high order interpolation scheme. The new limiting process was applied to numerous test cases. Through these tests, we could confirm that e-MLP enhances the accuracy and efficiency with both continuous and discontinuous multidimensional flows.

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