We establish well-posedness of a class of first order Hamilton-Jacobi equation in geodesic metric spaces. The result is then applied to solve a Hamilton-Jacobi equation in the Wasserstein space of probability measures, which arises from the variational formulation of a compressible Euler equation.

This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier–Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers’s equa...

The Dirac particle, i.e. the dynamic system SD, described by the free Dirac equation is investigated. Although the Dirac equation is written usually in the relativistically covariant form, the dynamic system SD is not completely relativistic, because its description contains such absolute objects as γ-matrices γk, forming a matrix vector. By means of the proper change of variables the γ-matrice...

This article presents a time-accurate numerical method using high-order accurate compact finite difference scheme for the incompressible Navier–Stokes equations. The method relies on the artificial compressibility formulation, which endows the governing equations a hyperbolic–parabolic nature. The convective terms are discretized with a third-order upwind compact scheme based on flux-difference...

As a continuous eeort to understand the Godunov-type schemes, following the paper \Projection in this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers. More speciically, the underlying dynamics of Flux Vector Splitting (FVS) and Flux Diierence Splitting (FDS) schemes will be analyzed. Since the FVS scheme and the Kinetic Flux Vector Splitting (...

The theory of compressible MHD (e.g., Alfvénic) turbulence has been a topic of interest for some time [1]. Alfvén wave turbulence presents several novel challenges, due to the fact the k–ω selection rules preclude three Alfvén-wave resonance. Thus, in incompressible MHD, two Alfvén waves can interact only with the vortex (i.e., eddy) mode. Compressibility relaxes this constraint by allowing int...

Numerical simulations of axisymmetric flows over reentry configurations at hypersonic conditions using a Navier-Stokes solver are presented. The Navier-Stokes equations are modified using Park’s two-temperature model to account for thermochemical nonequilibrium and weak ionization effects. The finite-volume method is used to solve the set of differential equations. The code has the capability t...

Numerical simulations of axisymmetric flows over the FIRE-II spacecraft at reentry conditions using a Navier-Stokes solver being developed at the University of Michigan are presented. The finite-volume method is used to solve the set of differential equations. The code has the capability to handle any mix of hexahedra, tetrahedra, prisms and pyramids in 3D or triangles and quadrilaterals in 2D....

A class of upwind flux splitting methods in the Euler equations of compressible flow is considered in this paper. Using the property that Euler flux F (U) is a homogeneous function of degree one in U , we reformulate the splitting fluxes with F+ = A+U , F− = A−U , and the corresponding matrices are either symmetric or symmetrizable and keep only non-negative and non-positive eigenvalues. That l...

We consider the compressible barotropic Navier-Stokes system in one dimension, with a nonmonotonic equation of state. The associated free boundary problem is investigated, and we prove asymptotic properties of the unique globally defined solution for large time. We also make some comments on a related model of quantum fluid describing the dynamics of cold nuclear matter (zero temperature). @ 20...