A convergent series expansion for hyperbolic systems of conservation laws

The discontinuities piecewise analytic initial value problem for a wide class of conservation laws is considered which includes the full three-dimensional Euler equations. The initial interaction at an arbitrary curved surface is resolved in time by a convergent series. Among other features the solution exhibits shock, contact, and expansion waves as well as sound waves propagating on characteristic surfaces. The expansion waves correspond to he one-dimensional rarefactions but have a more complicated structure. The sound waves are generated in place of zero strength shocks, and they are caused by mismatches in derivatives

Matched asymptotic expansions to similarity solutions of shock diffraction

Formal asymptotic expansions with differently scaled variables are matched to obtain a uniform approximation to the similarity solution of the shock-wedge diffraction problem

Computer simulations of ions in radio-frequency traps

The motion of ions in a trapped-ion frequency standard affects the stability of the standard. In order to study the motion and structures of large ion clouds in a radio-frequency (RF) trap, a computer simulation of the system that incorporates the effect of thermal excitation of the ions was developed. Results are presented from the simulation for cloud sizes up to 512 ions, emphasizing cloud structures in the low-temperature regime

Reducing Spurious Diapycnal Mixing in Ocean Models

Transport algorithms of numerical ocean circulation models are frequently exhibiting truncation errors leading to spurious diapycnal mixing of water masses. The chapter discusses methods that might be useful in diagnosing spurious diapycnal mixing and describes some approaches that might be helpful for its reduction. The first one is related to the use of the Arbitrary Lagrangian Eulerian (ALE) vertical coordinate which allows the implementation of vertically moving meshes that may partly follow the isopycnals even if the basic vertical coordinate differs from isopycnal. The second approach relies on modified advection schemes with the dissipative part of the transport operators directed isopycnally. Finally the third approach deals with new efficient and stable advection algorithms of arbitrary high order based on the WENO- ADER method, which can be applied to both structured and unstructured meshes. While practical benefits of using the reviewed approaches depend on applications, there are indications that equipping present state- of-the-art ocean circulation models with them would lead to reduced spurious transformations