Efficient higher order compact scheme for deforming unstructured meshes

1996 ◽  
Author(s):  
A. Boschitsch ◽  
T. Quackenbush
Keyword(s):  
Unstructured Meshes ◽  
Higher Order ◽  
Compact Scheme

Higher-order mimetic methods for unstructured meshes

2006 ◽  
Vol 219 (1) ◽  
pp. 68-85 ◽  
Author(s):  
V. Subramanian ◽  
J.B. Perot
Keyword(s):  
Unstructured Meshes ◽  
Higher Order

Numerical Study of Advection Schemes for Interface Capturing in a Volume of Fluid Method on Unstructured Meshes

2011 ◽  
Author(s):  
Hua Shan ◽  
Sung-Eun Kim
Keyword(s):  
Free Surface ◽  
Volume Fraction ◽  
Numerical Study ◽  
Volume Of Fluid ◽  
Unstructured Meshes ◽  
Higher Order ◽  
Numerical Dispersion ◽  
Numerical Dissipation ◽  
Interface Capturing ◽  
Advection Schemes

In solving naval hydrodynamics problems using computational fluid dynamics (CFD), the moving free surface between air and water introduces extra difficulties to numerical methods, since the material property jumps across the interface and the time-dependent free surface position becomes part of the solution. Engineering applications often require a flexible and robust solver for incompressible multi-phase viscous flows with the capability of capturing the interface. In the volume of fluid (VOF) method, the interface is captured by directly solving the convection transport equation of volume fraction. In this case, the numerical dissipation of the advection scheme smears the sharp interface and the numerical dispersion causes unphysical oscillations near the interface. Utilizing the guidance of boundedness criteria, many limited higher-order non-liner advection schemes have been developed in an attempt to balance numerical dissipation and dispersion. Though it is well-known that these non-linear advection schemes can lead to solutions combining boundednesss and accuracy, users are often overwhelmed by the wide variety of available schemes. Also, these schemes are developed with the assumption of a uniform Cartesian-type mesh. Thus, a thorough investigation and comparison of the performance of these interface-capturing advection schemes are necessary, especially for naval hydrodynamics problems solved on unstructured meshes. In this study, a systematic comparison and evaluation of several existing and new bounded, higher-order advection schemes has been conducted within the framework of NavyFOAM, which is developed based on OpenFOAM — an object orientated C++ toolbox for the customization and extension of numerical solvers for continuum mechanics problems, including CFD, where the governing equations are discretized using the cell-centered finite volume method on unstructured mesh. The flexible infrastructure of the code enables us to implement and test the selected advection schemes very quickly. The test cases include advection of hollow cylinders, Zalesak’s rotating slotted disk, traveling solitary wave, dam breaking problem.

scholarly journals Higher-order compact scheme for high-performance computing of stratified rotating flows

2018 ◽  
Vol 174 ◽  
pp. 300-310 ◽  
Author(s):  
Stéphane Abide ◽  
Stéphane Viazzo ◽  
Isabelle Raspo ◽  
Anthony Randriamampianina
Keyword(s):  
High Performance Computing ◽  
High Performance ◽  
Higher Order ◽  
Rotating Flows ◽  
Compact Scheme ◽  
Performance Computing
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