scholarly journals Numerical accuracy and hardware tradeoffs for CORDIC arithmetic for special-purpose processors

1993 ◽  
Vol 42 (7) ◽  
pp. 769-779 ◽  
Author(s):  
K. Kota ◽  
J.R. Cavallaro
1994 ◽  
Vol 144 ◽  
pp. 503-505
Author(s):  
R. Erdélyi ◽  
M. Goossens ◽  
S. Poedts

AbstractThe stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. Our computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code.


2020 ◽  
Vol 64 (1-4) ◽  
pp. 621-629
Author(s):  
Yingsong Zhao ◽  
Cherdpong Jomdecha ◽  
Shejuan Xie ◽  
Zhenmao Chen ◽  
Pan Qi ◽  
...  

In this paper, the conventional database type fast forward solver for efficient simulation of eddy current testing (ECT) signals is upgraded by using an advanced multi-media finite element (MME) at the crack edge for treating inversion of complex shaped crack. Because the analysis domain is limited at the crack region, the fast forward solver can significantly improve the numerical accuracy and efficiency once the coefficient matrices of the MME can be properly calculated. Instead of the Gauss point classification, a new scheme to calculate the coefficient matrix of the MME is proposed and implemented to upgrade the ECT fast forward solver. To verify its efficiency and the feasibility for reconstruction of complex shaped crack, several cracks were reconstructed through inverse analysis using the new MME scheme. The numerical results proved that the upgraded fast forward solver can give better accuracy for simulating ECT signals, and consequently gives better crack profile reconstruction.


2013 ◽  
Vol 284-287 ◽  
pp. 3345-3351
Author(s):  
Chi Chang Wang ◽  
Wu Jung Liao ◽  
Lu Ping Chao

This study used rectangular fins with constant heat transfer coefficient as material to discuss convective and radiative heat transfer, so as to prove that the hybrid spline difference method proposed in this study is an easy to operate method with high accuracy. According to the computational process described in this paper, the hybrid spline difference method is as simple as finite difference method and is easy to use. The complex computational process of traditional spline method can be simplified by using this method, but the numerical accuracy can be increased to second order. Therefore, the high accuracy numerical method of hybrid spline difference method replacing traditional spline method for future heat transfer analyses is expectable.


2007 ◽  
Vol 135 (11) ◽  
pp. 3876-3894 ◽  
Author(s):  
Ali R. Mohebalhojeh ◽  
David G. Dritschel

Abstract The representation of nonlinear shallow-water flows poses severe challenges for numerical modeling. The use of contour advection with contour surgery for potential vorticity (PV) within the contour-advective semi-Lagrangian (CASL) algorithm makes it possible to handle near-discontinuous distributions of PV with an accuracy beyond what is accessible to conventional algorithms used in numerical weather and climate prediction. The emergence of complex distributions of the materially conserved quantity PV, in the absence of forcing and dissipation, results from large-scale shearing and deformation and is a common feature of high Reynolds number flows in the atmosphere and oceans away from boundary layers. The near-discontinuous PV in CASL sets a limit on the actual numerical accuracy of the Eulerian, grid-based part of CASL. For the spherical shallow-water equations, the limit is studied by comparing the accuracy of CASL algorithms with second-order-centered, fourth-order-compact, and sixth-order-supercompact finite differencing in latitude in conjunction with a spectral treatment in longitude. The comparison is carried out on an unstable midlatitude jet at order one Rossby number and low Froude number that evolves into complex vortical structures with sharp gradients of PV. Quantitative measures of global conservation of energy and angular momentum, and of imbalance as diagnosed using PV inversion by means of Bolin–Charney balance, indicate that fourth-order differencing attains the highest numerical accuracy achievable for such nonlinear, advectively dominated flows.


2003 ◽  
Vol 125 (4) ◽  
pp. 723-730
Author(s):  
H. Nilsson ◽  
L. Davidson

This work derives and applies a method for the investigation of numerical accuracy in computational fluid dynamics. The method is used to investigate discretization errors in computations of swirling flow in water turbines. The work focuses on the conservation of a subset of the angular momentum equations that is particularly important to swirling flow in water turbines. The method is based on the fact that the discretized angular momentum equations are not necessarily conserved when the discretized linear momentum equations are solved. However, the method can be used to investigate the effect of discretization on any equation that should be conserved in the correct solution, and the application is not limited to water turbines. Computations made for two Kaplan water turbine runners and a simplified geometry of one of the Kaplan runner ducts are investigated to highlight the general and simple applicability of the method.


2013 ◽  
Vol 397-400 ◽  
pp. 270-273
Author(s):  
Ying Li ◽  
Xiao Bin Li ◽  
Yu Wang ◽  
Wei Zhang

Blast wave is numerical simulated based on FCT method. According to the comparative analysis, taking Henrych empirical formula as a standard, FCT method is more accuracy than Godunov method. Moreover, it has been found that the numerical accuracy is insufficient when the distance is small, it is necessary to develop and modify the numerical method continuously.


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