In this paper we propose a new numerical scheme to simulate the river flow in the presence of a variable bottom surface. We use the finite volume method, our approach is based on the technique described by D. L. George for shallow water equations. The main goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur. Furthermore this should preserve nonnegativity of some quantities, which are essentially nonnegative...
One of the commonly used models for river flow modelling is based on the Saint-Venant equations - the system of hyperbolic equations with spatially varying flux function and a source term. We introduce finite volume methods that solve this type of balance laws efficiently and satisfy some important properties at the same time. The properties like consistency, stability and convergence are necessary for the mathematically correct solution. However, the schemes should be also positive semidefinite...
The aim of this article is to briefly introduce the procedure for optimizing water turbine blades, which can lead to an innovative blade design and, consequently, an improvement in the desired properties of the water turbine, such as efficiency or the preferred pressure distribution on the blade. The computational method is based on formulating an objective function under certain constraint conditions, which are governed by the Navier-Stokes equations. This formulation enables the use of the Lagrange...
We propose a new numerical scheme based on the finite volumes to simulate the
urethra flow based on hyperbolic balance law. Our approach is based on the Riemann
solver designed for the augmented quasilinear homogeneous formulation. The scheme has general semidiscrete wave–propagation form and can be extended to arbitrary high order accuracy. The first goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur....
We derive the smoothed aggregation two-level method from the variational objective to minimize the final error after finishing the entire iteration. This contrasts to a standard variational two-level method, where the coarse-grid correction vector is chosen to minimize the error after coarse-grid correction procedure, which represents merely an intermediate stage of computing. Thus, we enforce the global minimization of the error. The method with smoothed prolongator is thus interpreted as a qualitatively...
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