A Simplified h-box Method for Embedded Boundary Grids

نویسندگان

  • Marsha J. Berger
  • Christiane Helzel
چکیده

We present a simplified h-box method for integrating time-dependent conservation laws on embedded boundary grids using an explicit finite volume scheme. By using a method of lines approach with a strong stability preserving Runge–Kutta method in time, the complexity of our previously introduced h-box method is greatly reduced. A stable, accurate, and conservative approximation is obtained by constructing a finite volume method where the numerical fluxes satisfy a certain cancellation property. For a model problem in one space dimension using appropriate limiting strategies, the resulting method is shown to be total variation diminishing. In two space dimensions, stability is maintained by using rotated h-boxes as introduced in previous work [M. J. Berger and R. J. LeVeque, Comput. Systems Engrg., 1 (1990), pp. 305–311; C. Helzel, M. J. Berger, and R. J. LeVeque, SIAM J. Sci. Comput., 26 (2005), pp. 785–809], but in the new formulation, h-box gradients are taken solely from the underlying Cartesian grid, which also reduces the computational cost.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Two-Dimensional Boundary-Conforming Orthogonal Grids for External and Internal Flows Using Schwarz-Christoffel Transformation

In this paper, a Schwarz-Christoffel method for generating two-dimensional grids for a variety of complex internal and external flow configurations based on the numerical integration procedure of the Schwarz-Christoffel transformation has been developed by using Mathematica, which is a general purpose symbolic-numerical-graphical mathematics software. This method is highly accurate (fifth order...

متن کامل

Two-Dimensional Boundary-Conforming Orthogonal Grids for External and Internal Flows Using Schwarz-Christoffel Transformation

In this paper, a Schwarz-Christoffel method for generating two-dimensional grids for a variety of complex internal and external flow configurations based on the numerical integration procedure of the Schwarz-Christoffel transformation has been developed by using Mathematica, which is a general purpose symbolic-numerical-graphical mathematics software. This method is highly accurate (fifth order...

متن کامل

A discontinuous Galerkin method for solutions of the Euler equations on Cartesian grids with embedded geometries

We present a discontinuous Galerkin method (DGM) for solutions of the Euler equations on Cartesian grids with embedded geometries. Cartesian grid methods can provide considerable computational savings for computationally intensive schemes like the DGM. Cartesian mesh generation is also simplified compared to the body fitted meshes. However, cutting an embedded geometry out of the grid creates c...

متن کامل

Equidistribution grids for two-parameter convection–diffusion boundary-value problems

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

متن کامل

A Simplified Curved Boundary Condition in Stationary/Moving Boundaries for the Lattice Boltzmann Method

Lattice Boltzmann method is one of computational fluid dynamic subdivisions. Despite complicated mathematics involved in its background, end simple relations dominate on it; so in comparison to the conventional computational fluid dynamic methods, simpler computer programs are needed. Due to its characteristics for parallel programming, this method is considered efficient for the simulation of ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • SIAM J. Scientific Computing

دوره 34  شماره 

صفحات  -

تاریخ انتشار 2012