We develop and analyze an improved version of the Multi-Stage (MUSTA) approach to the construction of upwind Godunov-type fluxes whereby the solution of the Riemann problem, approximate or exact, is not required. The new MUSTA schemes improve upon the original schemes in terms of monotonicity properties, accuracy and stability in multiple space dimensions. We incorporate the MUSTA technology in...

The purpose of this paper is twofold. Firstly we carry out an extension of the finite-volume WENO approach to three space dimensions and higher orders of spatial accuracy (up to eleventh order). Secondly, we propose to use three new fluxes as a building block in WENO schemes. These are the one-stage HLLC [29] and FORCE [24] fluxes and a recent multistage MUSTA flux [26]. The numerical results i...

Authentic Ativisha (Aconitum heterophyllum) is a rare, endangered Himalayan species. Ayurveda classical texts of c. 15(th)-16(th) century, introduced "abhava-pratinidhi dravya" concept, wherein Ativisha was categorized as an abhava dravya (unavailable drug) and Musta (Cyperus rotundus) was suggested as a pratinidhi dravya (substitute) for it. C. rotundus is a weed, abundantly available pan-Indi...

Using the concept of monotonization, families of two step and k-step finite volume schemes for scalar hyperbolic conservation laws are constructed and analyzed. These families contain the Force scheme and give an alternative to the Musta scheme. These schemes can be extended to systems of conservation law. Key-words: Finite volumes, finite differences, Riemann solvers, conservation laws, monoto...

This paper is devoted to the construction of numerical fluxes for hyperbolic systems. We first present a GFORCE numerical flux, which is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first order upwind method. Then we incorporate GFORCE in the framework of the...