A high-order finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM)
نویسندگان
چکیده
A hierarchy of one-dimensional high-order remapping schemes is presented and their performance with respect to accuracy and convergence rate investigated. The schemes are also compared based on remapping experiments in closed domains. The piecewise quartic method (PQM) is presented, based on fifth-order accurate piecewise polynomials, and is motivated by the need to significantly improve hybrid coordinate systems of ocean climate models, which require the remapping to be conservative, monotonic and highly accurate. A limiter for this scheme is fully described that never decreases the polynomial degree, except at the location of extrema. We assess the use of high-order explicit and implicit (i.e., compact) estimates for the edge values and slopes needed to build the piecewise polynomials in both piecewise parabolic method (PPM) and PQM. It is shown that all limited PQM schemes perform significantly better than limited PPM schemes and that PQM schemes are much more cost-effective. 2008 Elsevier Inc. All rights reserved.
منابع مشابه
Time-splitting framework for Godunov-type finite- volume non-hydrostatic atmospheric models
Highorder extensions of the classical Godunov scheme offer computationally attractive features including inherent conservation, geometric flexibility, and accuracy for solving hyperbolic conservation laws. The Godunov-type methods typically do not rely on staggered grids, and the cellaveraged solution is not assumed to be continuous across the cell (control volume) edges. The discontinuity of t...
متن کاملA Mass Conservative Method for Numerical Modeling of Axisymmetric flow
In this paper, the cell-centered finite volume method (CC-FVM) has been presented to simulate the axisymmetric radial flow toward a pumping well. The model is applied to the unstructured triangular grids which allows to simulate inhomogeneous and complex-shaped domains. Due to the non-orthogonality of the irregular grids, the multipoint flux approximation (MPFA) methods are used to discretize t...
متن کاملAdaptive Unstructured Grid Generation Scheme for Solution of the Heat Equation
An adaptive unstructured grid generation scheme is introduced to use finite volume (FV) and finite element (FE) formulation to solve the heat equation with singular boundary conditions. Regular grids could not acheive accurate solution to this problem. The grid generation scheme uses an optimal time complexity frontal method for the automatic generation and delaunay triangulation of the grid po...
متن کاملWell-balanced Finite Volume Evolution Galerkin Methods for the 2d Shallow Water Equations on Adaptive Grids
Abstract. We extend a well-balanced finite volume evolution Galerkin (FVEG) method to nonuniform grids. As a model problem, we consider the two-dimensional shallow water equations with a source term modelling the bottom topography. Our work is based on the well-balanced scheme proposed in (Lukáčová, Noelle, Kraft, J.Comp.Physics, 221, 2007). We present selected test cases to demonstrate the cap...
متن کاملConvergence of a Finite Volume Extension of the Nessyahu–tadmor Scheme on Unstructured Grids for a Two-dimensional Linear Hyperbolic Equation∗
Abstract. The nonoscillatory central difference scheme of Nessyahu and Tadmor is a Godunovtype scheme for one-dimensional hyperbolic conservation laws in which the resolution of Riemann problems at the cell interfaces is bypassed thanks to the use of the staggered Lax–Friedrichs scheme. Piecewise linear MUSCL-type (monotonic upstream-centered scheme for conservation laws) cell interpolants and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comput. Physics
دوره 227 شماره
صفحات -
تاریخ انتشار 2008