Hybrid Methods for Computing the Streamfunction and Velocity Potential for Complex Flow Fields over Mesoscale Domains

Abstract

AbstractThree types of previously used numerical methods are revisited for computing the streamfunction ψ and velocity potential χ from the horizontal velocity v in limited domains. The first type, called the SOR-based method, uses a classical successive over-relaxation (SOR) scheme to compute ψ (or χ) first with an arbitrary boundary condition (BC) and then χ (or ψ) with the BC derived from ν. The second type, called the spectral method, uses spectral formulations to construct the inner part of (ψ, χ)—the inversion of (vorticity, divergence) with a homogeneous BC, and then the remaining harmonic part of (ψ, χ) with BCs from ν. The third type, called the integral method, uses integral formulas to compute the internally induced (ψ, χ)—the inversion of domain-internal (vorticity, divergence) using the free-space Green’s function without BCs and then the remaining harmonic ψ (or χ) with BCs from v minus the internally-induced part. Although these methods have previously been successfully applied to flows in large-scale and synoptic-scale domains, their accuracy is compromised when applied to complex flows over mesoscale domains, as shown in this paper. To resolve this problem, two hybrid approaches, the integral-SOR method and the integral-spectral method, are developed by combining the first step of the integral method with the second step adopted from the SOR-based and spectral methods, respectively. Upon testing these methods on real-case complex flows, the integral-SOR method is significantly more accurate than the integral-spectral method, noting that the latter is still generally more accurate than the three previously-used methods. The integral-SOR method is recommended for future applications and diagnostic studies of complex flows.