In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla and known as deferred correction, has been intensively utilized by Muzaferija and later Fergizer and Peric to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of t...

Based on general partitions of unity and standard numerical flux functions, a class of mesh-free methods for conservation laws is derived. A Lax-Wendroff type consistency analysis is carried out for the general case of moving partition functions. The analysis leads to a set of conditions which are checked for the finite volume particle method FVPM. As a by-product, classical finite volume schem...

This paper is concerned with the development and study of a stabilized finite volume method for the transient Stokes problem in two and three dimensions. The stabilization is based on two local Gauss integrals and is parameter-free. The analysis is based on a relationship between this new finite volume method and a stabilized finite element method using the lowest equal-order pair (i.e., the P1...

Abstract. In this paper we investigate symmetry-preserving boundary conditions for a fourth-order symmetry-preserving finite volume method, to able to do accurate turbulence simulations for wind-turbine wake applications. It is found that the use of Dirichlet conditions limits the fourth-order method to (at most) second order. However, on properly chosen non-uniform grids, fourth-order behavior...

Hybrid finite volume/element methods are investigated within the context of transient viscoelastic flows. A finite volume algorithm is proposed for the hyperbolic constitutive equation, of Oldroyd-form, whilst the continuity/momentum balance is accommodated through a TaylorGalerkin finite element method. Various finite volume combinations are considered to derive accurate and stable implementat...

There are three important steps in the computational modelling of any physical process: (i) problem definition, (ii) mathematical model, and (iii) computer simulation. The first natural step is to define an idealization of our problem of interest in terms of a set of relevant quantities which we would like to measure. In defining this idealization we expect to obtain a well-posed problem, this ...

II. Foundations 5 A. The Mathematical Structure of Physical Field Theories . . . 5 B. Geometric Objects and Orientation . . . . . . . . . . . . . 7 C. Physical Laws and Physical Quantities . . . . . . . . . . . . 15 D. Classification of Physical Quantities . . . . . . . . . . . . . 21 E. Topological Laws . . . . . . . . . . . . . . . . . . . . . . . 26 F. Constitutive Relations . . . . . . . . ...