• 한국해양공학회지
• /
• 제25권5호
• /
• pp.9-14
• /
• 2011

The divergence-free finite elements introduced in this paper are derived from Hermite functions, which interpolate stream functions. Velocity bases are derived from the curl of the Hermite functions. These velocity basis functions constitute a solenoidal function space, and the gradient of the Hermite functions constitute an irrotational function space. The incompressible Navier-Stokes equation is orthogonally decomposed into its solenoidal and irrotational parts, and the decoupled Navier-Stokes equations are then projected onto their corresponding spaces to form appropriate variational formulations. The degrees of the Hermite functions we introduce in this paper are bi-cubis, quartic, and quintic. To verify the accuracy and convergence of the present method, three well-known benchmark problems are chosen. These are lid-driven cavity flow, flow over a backward facing step, and buoyancy-driven flow within a square enclosure. The numerical results show good agreement with the previously published results in all cases.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2006년도 추계 학술대회논문집
• /
• pp.61-65
• /
• 2006

This paper describes a recent development on the divergence free basis function based on a hermite stream function. The well-known cavity problem has been used to compare the accuracy and the convergence of the present method with those of a modified residual method known as one of the stabilized finite element methods. The comparison showed the present method performs better in the accuracy and convergence.

• 한국해양공학회:학술대회논문집
• /
• 한국해양공학회 2006년 창립20주년기념 정기학술대회 및 국제워크샵
• /
• pp.411-414
• /
• 2006

This paper describes a recent development on the divergence free basis function based on a hermite stream function. The well-known cavity problem has been used to compare the accuracy and the convergence of the present method with those of a modified residual method known as one of the stabilized finite e1ement methods. The comparison showed the present method performs better in the accuracy and convergence.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2007년도 추계 학술대회논문집
• /
• pp.220-225
• /
• 2007

This paper is a continuation of the recent development on the hermite-based divergence free basis function and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square cavity with temperature difference across the two sides. The basis functions for the velocities consist of the hermite function and its curl. However, the basis for the temperature are the hermite function and its gradienst. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x- and y-derivatives. Numerical results for the streamlines, the temperatures, the x-velocities and the y-velocities show good agreements with those of De vahl Davis[7].

• 한국전산유체공학회지
• /
• 제12권1호
• /
• pp.35-42
• /
• 2007

This paper describes a recent development on the divergence free basis function based on a hermite stream function and verifies its validity by comparing results with those from a modified residual method known as one of stabilized finite element methods. It can be shown that a proper choice of degrees of freedom at a node with a proper arrangement of the hermite interpolation functions can yield solenoidal or divergent free interpolation functions for the velocities. The well-known cavity problem has been chosen for validity of the present algorithm. The comparisons from numerical results between the present and the modified residual showed the present method yields better results in both the velocity and the pressure within modest Reynolds numbers(Re = 1,000).

• 마이크로전자및패키징학회지
• /
• 제27권4호
• /
• pp.47-54
• /
• 2020

활성 도파로와 수동 도파로의 집적은 광집적 회로의 구성에서 필수적인 요소이다. 이를 구현하기 위한 여러 기술 중 버트 조인트는 상당한 장점을 가지고 있다. 그러나 버트 조인트 접합은 높은 광손실을 야기하며, 두 도파로 간의 정렬에 있어서 정확한 공정 제어가 요구되는 구조이다. 본 논문에서는 레이저 다이오드와 spot size converter (SSC)로 구성된 집적 소자를 시뮬레이션하기 위해 beam propagation method을 이용하였다. 상이한 모드 특성을 갖는 두 SSC를 레이저 도파로와 연결하고, 광결합 효율을 시뮬레이션 하였다. 큰 근접장 모드를 가지는 SSC는 낮은 광결합 효율을 보여주나, 원거리 발산각 패턴이 좁고 더 대칭적이다. 테이퍼 구조의 수동 도파로는 원거리 발산각 패턴을 열화시키지 않고 버트 조인트에서 도파로 오프셋의 무의존성과 광결합 효율을 향상시키기 위해 이용되었다. 이를 바탕으로 89.6%의 높은 광결합 효율과 16°×16°의 좁은 원거리장 발산각을 얻을 수 있었다.

• 한국해양공학회지
• /
• 제23권5호
• /
• pp.1-8
• /
• 2009

This paper is a continuation of the recent development on Hermite-based divergence free element method and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square enclosure with temperature difference across the two sides. The basis functions for the velocity field consist of the Hermite function and its curl while the basis functions for the temperature field consists of the Hermite function and its gradients. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x and y derivatives. This paper presents numerical results for Ra = 105, and compares with those from a stabilized finite element method developed by Illinca et al. (2000). The comparison has been done on 32 by 32 uniform elements and the degree of approximation of elements used for the stabilized finite element are linear (Deg. 1) and quadratic (Deg. 2). The numerical results from both methods show well agreements with those of De vahl Davi (1983).

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2008년도 학술대회
• /
• pp.33-41
• /
• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2008년 추계학술대회논문집
• /
• pp.33-41
• /
• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• 한국전산유체공학회지
• /
• 제14권4호
• /
• pp.67-77
• /
• 2009

This paper is a continuation of a recent development on the Hermite-based divergence-free element method and deals with a non-isothermal fluid flow driven by the buoyancy force in a square cavity with temperature difference across the two sides. Two Hermite functions are considered for numerical computations in this paper. One is a cubic function and the other is a quartic function. The degrees-of-freedom of the cubic Hermite function are stream function and its first and second derivatives for the velocity field, and temperature and its first derivatives for the temperature field. The degrees-of-freedom of the quartic Hermite function include two second derivatives and one cross derivative of the stream function in addition to the degrees-of-freedom of the cubic stream function. This paper presents a brief review on the Hermite based divergence-free basis functions and its finite element formulations for the buoyancy driven flow. The present algorithm does not employ any upwinding or a stabilization term. However, numerical values and contour graphs for major flow variables showed good agreements with those by De Vahl Davis[6].