13 research outputs found
On the essential role of kinetic theory in numerical methods for fluid-dynamic equations
The essential role of kinetic theory in the numerical methods for the Navier‐Stokes equations (compressible and incompressible) is discussed. The easy theory of characteristics for kinetic equations brings about drastic simplification of approximate Riemann solver employed in various shock‐capturing schemes. The lattice Boltzmann method is shown to essentially solve an artificial compressibility PDE system. The asymptotic behavior of solution of kinetic equations for small mean free path does not play the essential role in these kinetic numerical methods
Link-wise Artificial Compressibility Method
The Artificial Compressibility Method (ACM) for the incompressible
Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by
a finite set of discrete directions (links) on a regular Cartesian mesh, in
analogy with the Lattice Boltzmann Method (LBM). The main advantage is the
possibility of exploiting well established technologies originally developed
for LBM and classical computational fluid dynamics, with special emphasis on
finite differences (at least in the present paper), at the cost of minor
changes. For instance, wall boundaries not aligned with the background
Cartesian mesh can be taken into account by tracing the intersections of each
link with the wall (analogously to LBM technology). LW-ACM requires no
high-order moments beyond hydrodynamics (often referred to as ghost moments)
and no kinetic expansion. Like finite difference schemes, only standard Taylor
expansion is needed for analyzing consistency. Preliminary efforts towards
optimal implementations have shown that LW-ACM is capable of similar
computational speed as optimized (BGK-) LBM. In addition, the memory demand is
significantly smaller than (BGK-) LBM. Importantly, with an efficient
implementation, this algorithm may be one of the few which is compute-bound and
not memory-bound. Two- and three-dimensional benchmarks are investigated, and
an extensive comparative study between the present approach and state of the
art methods from the literature is carried out. Numerical evidences suggest
that LW-ACM represents an excellent alternative in terms of simplicity,
stability and accuracy.Comment: 62 pages, 20 figure
Artificial Compressibility Method Revisited: Asymptotic Numerical Method for Incompressible Navier-Stokes Equations
STRUCTURE OF NORMAL SHOCK WAVES(Mathematical Analysis of Phenomena in Fluid and Plasma Dynamics)
Artificial Compressibility Method Revisited: Theory of Asymptotic Numerical Method for the Incompressible Navier-Stokes Equations
Artificial Compressibility Method Revisited: Theory of Asymptotic Numerical Method for the Incompressible Navier-Stokes Equations
Numerical examination of applicability of the linearized Boltzmann equation(Mathematical Analysis of Phenomena in Fluid and Plasma Dynamics)
EVAPORATION AND CONDENSATION OF A RAREFIED GAS BETWEEN ITS TWO PARALLEL PLANE CONDENSED PHASES WITH DIFFERENT TEMPERATURES AND NEGATIVE TEMPERATURE-GRADIENT PHENOMENON : NUMERICAL ANALYSIS OF THE BOLTZMANN EQUATION FOR HARD-SPHERE MOLECULES(Mathematical Analysis of Fluid and Plasma Dynamics)
On the remedy against shock anomalies in kinetic schemes
Shock-capturing schemes often exhibit anomalous behaviors, such as the carbuncle phenomenon and the post-shock oscillations, especially in the hypersonic flow regime. This paper proposes a simple and effective remedy against these shock instabilities in the case of the kinetic Lax-Wendroff scheme, where the well-known classic scheme is reinforced by means of an equilibrium distribution function of gas molecules. The pathologies are significantly improved to an acceptable level for practical purposes without any considerable side-effect by locally bringing out the robustness of the equilibrium flux method from the kinetic scheme. The remedy is applied only to the preprocessing of the data at cell-edges. The performance of the fortified kinetic scheme is demonstrated in the problem of a hypersonic inviscid or viscous flow past a blunt body. Comparisons are also made with various advanced shock-capturing schemes at present. (c) 2013 Elsevier Inc. All rights reserved