• East Asian mathematical journal
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• 제34권5호
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• pp.601-614
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• 2018

In this paper, we introduce an extrapolated higher order characteristic finite element method to approximate solutions of nonlinear Sobolev equations with a convection term and we establish the higher order of convergence in the temporal and the spatial directions with respect to $L^2$ norm.

• 한국전산유체공학회지
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• 제19권3호
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• pp.52-61
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• 2014

The present paper deals with the efficient computation of higher-order CFD methods for compressible flow using graphics processing units (GPU). The higher-order CFD methods, such as discontinuous Galerkin (DG) methods and correction procedure via reconstruction (CPR) methods, can realize arbitrary higher-order accuracy with compact stencil on unstructured mesh. However, they require much more computational costs compared to the widely used finite volume methods (FVM). Graphics processing unit, consisting of hundreds or thousands small cores, is apt to massive parallel computations of compressible flow based on the higher-order CFD methods and can reduce computational time greatly. Higher-order multi-dimensional limiting process (MLP) is applied for the robust control of numerical oscillations around shock discontinuity and implemented efficiently on GPU. The program is written and optimized in CUDA library offered from NVIDIA. The whole algorithms are implemented to guarantee accurate and efficient computations for parallel programming on shared-memory model of GPU. The extensive numerical experiments validates that the GPU successfully accelerates computing compressible flow using higher-order method.

• 대한조선학회논문집
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• 제29권4호
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• pp.58-65
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• 1992

본 논문에서는 물체표면을 겹 3차 B-Spline 방법에 의하여 표현하고, 특이점세기를 겹선형으로 근사하는 고차판요소법을 이용하여 몰수체에 대한 조파저항을 계산하였다. 여기서 Neumann-kelvin 문제는 쏘오스분포법과 법선다이폴분포법에 의하여 해석되었다. 고차 판요소법에 의하여 계산된 결과는 Hess & Smith가 사용한 최저차 판요소법 결과와 비교하였으며, 고차 판요소법의 수렴도는 보통 판요소법보다 훨씬 좋은 것으로 나타났다. 그러나, 고차 판요소법에 의하여 계산된 조파저항도 최저차 판요소법에 의한 것과 마찬가지로 낮은 Froude 수에서는 해석해와의 차이를 보이고 있다.

• 소음진동
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• 제9권2호
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• pp.340-347
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• 1999

The acoustic performance of reactive type single expansion chamber can be calculated theoretically by plane wave theory. But higher order model should be considered to widen the frequency range. Mode matching method has been developed to consider higher order modes, but very complicated algebra should be used. Munjal suggested a numerical collocation method, which can overcome the shortcomings of mode matching method, using the compatibility conditions for acoustic pressure and particle velocity at the junctions of area discontinuities. But the restriction of Munjal's method is that the ratio between the area of inlet(or outlet) pipe and that of chamber must be natural number. In this paper, the new method was suggested to overcome the shortcomings of Munjal's method. The predictions by this method was also compared with those by the finite element method and Munjal's method in order to demonstrate the accuracy of the modified method presented here.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.61-62
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• 2003

In this paper, the new higher order wall boundary conditions are proposed for solving the incompressible flows. The square driven cavity flows are simulated by using the variable order method of lines with the present wall boundary conditions. The variable order method of lines is constructed by the spatial discretization, i.e., the variable order proper convective scheme for convective terms and the modified differential quadrature method for diffusive terms, and time integration. The 2nd, 4th, and 6th order solutions are presented and these results show this higher order boundary conditions are very promising for the incompressible flow simulations.

• East Asian mathematical journal
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• 제33권5호
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• pp.511-525
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• 2017

We introduce an extrapolated higher order characteristic finite element method to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergence in both the temporal direction and the spatial direction in $L^2$ normed space is established and some computational results to support our theoretical results are presented.

• 대한기계학회논문집A
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• 제24권5호
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• pp.1314-1322
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• 2000

The acoustic property of reactive type single expansion chamber can be analyzed by traditional plane wave theory. This theory can be applied in low frequency range and has good performance. But this theory can't include higher order modes, therefore another method is essential to analyze acoustic filter in high frequency range. Many researcher suggested the method that can concern higher order modes, and their methods are using mode matching technique. But there is no method that can be applied to the analysis of single expansion chamber with arbitrary inlet/outlet duct position and numbers of higher order modes of inlet/outlet duct and middle chamber. In this paper, the method which can analyze single expansion chamber with arbitrary inlet/outlet duct position and numbers of higher order modes of inlet/outlet duct and middle chamber using fundamental mode matching technique, was suggested and the predictions by this method was compared with those by the finite element method, and the influence of inlet/outlet location to acoustic performance of single expansion chamber is investigated and explained by higher order mode effects.

• 대한수학회보
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• 제50권3호
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• pp.963-982
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• 2013

The Galerkin method has been developed mainly for 2nd order differential equations. To get numerical solutions, there are some choices of Riesz bases for the approximation subspace $V_j{\subset}L^2$. In this paper we shall propose a uniform approach to find suitable Riesz bases for higher order differential equations. Especially for the beam equation (4-th order equation), we also report numerical results.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2007년도 춘계 학술대회논문집
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• pp.30-40
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• 2007

The implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes, which can achieve higher-order accuracy by wing hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. And, the flows around a circle and a NACA0012 airfoil was also numerically simulated. Numerical results show that the implicit discontinuous Galerkin methods with higher-order representation of curved solid boundaries can be an efficient higher-order method to obtain very accurate numerical solutions on unstructured meshes.

• 한국정밀공학회지
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• 제23권1호
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• pp.105-112
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• 2006

The nonlinear damping force model is made to identify the properties of the ER (electro-rheological) fluid suspension damper. The instrumentation is carried out to measure the damping force of the ER damper. The higher order spectral analysis method is used to investigate the nonlinear frequency coupling phenomena with the damping force signal according to the sinusoidal excitation of the damper. The distinctive higher order nonlinear characteristics are observed. The nonlinear damping force model, which has the higher order velocity terms, is proposed with the result of higher order spectrum analysis. The higher order terms coefficients, which vary according to the strength of the electric field, are calculated using the least square method.