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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.23 No.2
- 발행연도
- 2019.6
- 수록면
- 93 - 114 (22page)
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초록· 키워드
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In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion.
We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences.
The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first- order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.
We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences.
The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first- order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.
목차
ABSTRACT
1. INTRODUCTION
2. INVESTIGATION ON THE STRONG L²-STABILITY OF EXPLICIT SECOND ORDERSCHEMES FOR CONVECTION EQUATION
3. MODIFIED IMPLICIT RUNGE-KUTTA METHOD
4. MODIFIED IMPLICIT RK2 METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
5. NUMERICAL EXPERIMENTS
6. CONCLUSION
REFERENCES
참고문헌 (19)
참고문헌 신청
B. Lee / 2018 / An energy-stable method for solving the incompressible navier-stokes equations with non-slip boundary condition / Journal of Computational Physics 360:104~119
A. W. J. Carlson / 2006 / The millennium prize problems / American Mathematical Soc.
G. Ansanay-Alex / 2011 / An l2-stable approximation of the navier–stokes convection operator for low-order non-conforming finite elements / International Journal for Numerical Methods in Fluids 66(5):555~580
R. Herbin / 2010 / Kinetic energy control in the mac discretization of compressible navier-stokes equations / International Journal on Finite Volumes 7(2)
M. Gunzburger / 2017 / A second-order time-stepping scheme for simulating ensembles of parameterized flow problems / Computational Methods in Applied Mathematics
A. W. J. Carlson / 2006 / The millennium prize problems / American Mathematical Soc.
G. Ansanay-Alex / 2011 / An l2-stable approximation of the navier–stokes convection operator for low-order non-conforming finite elements / International Journal for Numerical Methods in Fluids 66(5):555~580
R. Herbin / 2010 / Kinetic energy control in the mac discretization of compressible navier-stokes equations / International Journal on Finite Volumes 7(2)
M. Gunzburger / 2017 / A second-order time-stepping scheme for simulating ensembles of parameterized flow problems / Computational Methods in Applied Mathematics
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UCI(KEPA) : I410-ECN-0101-2019-410-000881504