A forward-in-time advection scheme and adaptive multilevel flow solver for nearly incompressible atmospheric flow

Journal Article · Sun Dec 01 04:00:00 EST 1996 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1996.0250· OSTI ID:530641

Stevens, D E ^[1]; Bretherton, S ^[2]

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1. Lawrence Berkeley National Lab., CA (United States)
2. Univ. of Washington, Seattle, WA (United States)

This paper presents a new forward-in-time advection method for nearly incompressible flow, MU, and its application to an adaptive multilevel flow solver for atmospheric flows. MU is a modification of Leonard et al.`s UTOPIA scheme. MU, like UTOPIA, is based on third-order accurate semi-Lagrangian multidimensional upwinding for constant velocity flows. for varying velocity fields, MU is a second-order conservative method. MU has greater stability and accuracy than UTOPIA and naturally decomposes into a monotone low-order method and a higher-order accurate correction for use with flux limiting. Its stability and accuracy make it a computationally efficient alternative to current finite-difference advection methods. We present a fully second-order accurate flow solver for the anelastic equations, a prototypical low Mach number flow. The flow solver is based on MU which is used for both momentum and scalar transport equations. This flow solver can also be implemented with any forward-in-time advection scheme. The multilevel flow solver conserves discrete global integrals of advected quantities and includes adaptive mesh refinements. Its second-order accuracy is verified using a nonlinear energy conservation integral for the anelastic equations. For a typical geophysical problem in which the flow is most rapidly varying in a small part of the domain, the multilevel flow solver achieves global accuracy comparable to uniform-resolution simulation for 10% of the computational cost. 36 refs., 10 figs.

• OSTI ID: 530641
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 129; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
ADVECTION
ALGORITHMS
ATMOSPHERIC CIRCULATION
FLOW MODELS
INCOMPRESSIBLE FLOW
ITERATIVE METHODS
PARTIAL DIFFERENTIAL EQUATIONS