Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems

Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge-Kutta schemes available in literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.Comment: 37 pages, 3 pages of appendi

More efficient time integration for Fourier pseudo-spectral DNS of incompressible turbulence

Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge--Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher-order Runge-Kutta pairs and automatic step size control based on local error estimation. We find that the fifth-order accurate Runge--Kutta pair of Bogacki \& Shampine gives much greater accuracy at a significantly reduced computational cost. Specifically, we demonstrate speedups of 2x-10x for the same accuracy. Numerical tests (including the Taylor-Green vortex, Rayleigh-Taylor instability, and homogeneous isotropic turbulence) confirm the reliability and efficiency of the method. We also show that adaptive time stepping provides a significant computational advantage for some problems (like the development of a Rayleigh-Taylor instability) without compromising accuracy

A hybrid discrete exterior calculus and finite difference method for anelastic convection in spherical shells

The present work develops, verifies, and benchmarks a hybrid discrete exterior calculus and finite difference (DEC-FD) method for density-stratified thermal convection in spherical shells. Discrete exterior calculus (DEC) is notable for its coordinate independence and structure preservation properties. The hybrid DEC-FD method for Boussinesq convection has been developed by Mantravadi et al. (Mantravadi, B., Jagad, P., & Samtaney, R. (2023). A hybrid discrete exterior calculus and finite difference method for Boussinesq convection in spherical shells. Journal of Computational Physics, 491, 112397). Motivated by astrophysics problems, we extend this method assuming anelastic convection, which retains density stratification; this has been widely used for decades to understand thermal convection in stars and giant planets. In the present work, the governing equations are splitted into surface and radial components and discrete anelastic equations are derived by replacing spherical surface operators with DEC and radial operators with FD operators. The novel feature of this work is the discretization of anelastic equations with the DEC-FD method and the assessment of a hybrid solver for density-stratified thermal convection in spherical shells. The discretized anelastic equations are verified using the method of manufactured solution (MMS). We performed a series of three-dimensional convection simulations in a spherical shell geometry and examined the effect of density ratio on convective flow structures and energy dynamics. The present observations are in agreement with the benchmark models.Comment: 32 pages, 13 figure

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Gastro-intestinal helminths of pigeons (Columba livia) in Gujarat, India

A study was conducted to assess the prevalence of helmith parasites of domestic wild and zoo pigeons in Gujarat, India by faecal sampling and postmortem examination. Qualitative examination of 78 faecal samples revealed 71 (91%) with parasitic infections of nematodes (85%), cestodes (31%) and Eimeria sp (77%). There were 200-1600 nematode eggs per gram during the monsoon season, which was high compared to the 200-1000 eggs per gram in winter and summer. In post-mortems 85% had parasitic infections, of nematodes (75%), cestodes (69%) and Eimeria sp (58%). Two species of nematodes (Ascaridia columbae and Capillaria obsignata) and five species of three genera of cestodes (Raillietina echinobothridia, R. tetragona, R. cesticillus, Cotugnia digonophora and Hymenolepis sp) were identified. Despite their parasitic infections, not a single pigeon revealed any alarming clinical signs

Studies on gastro-intestinal helminths of Equus acinus in North Gujarat, India

A year round study (October to September) was conducted in the districts of North Gujarat (India) to identify the gastro-intestinal helminths of donkeys (Equus acinus), determine prevalence and correlate haematological parameters with parasite burdens. A total of 1794 faecal samples of donkeys contained the following helminths (prevalence % in brackets): Strongyloides westeri (17.2), Parascaris equorum (23.8), Strongylus sp. (55.3), an amphistome digenean (1.5), Anoplocephala sp. (1.0), Balantidium coli (13.1) and Eimeria leuckarti (7.0). Overall prevalence was 75.9 with a mean of 627 (50-1650) eggs per gram faeces. Seasonally the maximum prevalence (85.3) occurred in March and minimum (65.2) in July. 14% of donkeys were considered to be severely infected, 38% heavily, 36% moderately and 12% mildly infected. Larval cultures revealed the presence of (prevalence%): Cyathostomum sp. (48), Gyalocephalus sp. (8), Oesophagodontus sp. (6), Triodontophorus sp. (10), Strongyloides westeri (10), Strongylus vulgaris (30), Strongylus equines (40) and S. edentatus (30). Hematological indices were inversely proportional to epg counts.Keywords: donkeys, gastro-intestinal parasites, haematology, prevalence