Stability of preconditioned finite volume schemes at low Mach numbers

In [4], Guillard and Viozat propose a finite volume method for the simulation of inviscid steady as well as unsteady flows at low Mach numbers, based on a preconditioning technique. The scheme satisfies the results of a single scale asymptotic analysis in a discrete sense and comprises the advantage that this can be derived by a slight modification of the dissipation term within the numerical flux function. Unfortunately, it can be observed by numerical experiments that the preconditioned approach combined with an explicit time integration scheme turns out to be unstable if the time step Dt does not satisfy the requirement to be O(M2) as the Mach number M tends to zero, whereas the corresponding standard method remains stable up to Dt=O(M), M to 0, which results from the well-known CFL-condition. We present a comprehensive mathematical substantiation of this numerical phenomenon by means of a von Neumann stability analysis, which reveals that in contrast to the standard approach, the dissipation matrix of the preconditioned numerical flux function possesses an eigenvalue growing like M-2 as M tends to zero, thus causing the diminishment of the stability region of the explicit scheme. Thereby, we present statements for both the standard preconditioner used by Guillard and Viozat [4] and the more general one due to Turkel [21]. The theoretical results are after wards confirmed by numerical experiments.

Sulfur transfer and activation by ubiquitin-like modifier system Uba4•Urm1 link protein urmylation and tRNA thiolation in yeast

Urm1 is a unique dual-function member of the ubiquitin protein family and conserved from yeast to man. It acts both as a protein modifier in ubiquitin-like urmylation and as a sulfur donor for tRNA thiolation, which in concert with the Elongator pathway forms 5-methoxy-carbonyl-methyl-2-thio (mcm5s2) modified wobble uridines (U34) in anticodons. Using Saccharomyces cerevisiae as a model to study a relationship between these two functions, we examined whether cultivation temperature and sulfur supply previously implicated in the tRNA thiolation branch of the URM1 pathway also contribute to proper urmylation. Monitoring Urm1 conjugation, we found urmylation of the peroxiredoxin Ahp1 is suppressed either at elevated cultivation temperatures or under sulfur starvation. In line with this, mutants with sulfur transfer defects that are linked to enzymes (Tum1, Uba4) required for Urm1 activation by thiocarboxylation (Urm1-COSH) were found to maintain drastically reduced levels of Ahp1 urmylation and mcm5s2U34 modification. Moreover, as revealed by site specific mutagenesis, the Stransfer rhodanese domain (RHD) in the E1-like activator (Uba4) crucial for Urm1-COSH formation is critical but not essential for protein urmylation and tRNA thiolation. In sum, sulfur supply, transfer and activation chemically link protein urmylation and tRNA thiolation. These are features that distinguish the ubiquitin-like modifier system Uba4•Urm1 from canonical ubiquitin family members and will help elucidate whether, in addition to their mechanistic links, the protein and tRNA modification branches of the URM1 pathway may also relate in function to one another.