This study aimed to analyse the geographical distribution of COVID-19 and to identify highrisk areas in space and time for the occurrence of cases and deaths in the indigenous population of Brazil. This is an ecological study carried out between 24 March and 26 October 2020 whose units of analysis were the Special Indigenous Sanitary Districts. The Getis-Ord General G and Getis-Ord Gi* techniques were used to verify the spatial association of the phenomena and a retrospective space−time scan was performed. There were 32041 confirmed cases of COVID-19 and 471 deaths. The non-randomness of cases (z score = 5.40; p <0.001) and deaths (z score = 3.83; p <0.001) were confirmed. Hotspots were identified for cases and deaths in the north and midwest regions of Brazil. Sixteen high-risk space−time clusters were identified for the occurrence of cases with a higher RR=21.23 (p <0.001) and four risk clusters for deaths with a higher RR=80.33 (p <0.001). These clusters were identified from 22 May and were active until 10 October 2020. The results indicate critical areas in the indigenous territories of Brazil and contribute to better directing the actions of control of COVID-19 in this population.

The immersed boundary method has attracted considerable interest in the last few years. The method is a computational cheap alternative to represent the boundaries of a geometrically complex body, while using a cartesian mesh, by adding a force term in the momentum equation. The advantage of this is that bodies of any arbitrary shape can be added without grid restructuring, a procedure which is often time-consuming. Furthermore, multiple bodies may be simulated, and relative motion of those bodies may be accomplished at reasonable computational cost. The numerical platform in development has a parallel distributed-memory implementation to solve the Navier-Stokes equations. The Finite Volume Method is used in the spatial discretization where the diffusive terms are approximated by the central difference method. The temporal discretization is accomplished using the Adams-Bashforth method. Both temporal and spatial discretizations are second-order accurate. The Velocity-pressure coupling is done using the fractional-step method of two steps. The present work applies the immersed boundary method to simulate a Newtonian laminar flow through a three-dimensional sudden contraction. Results are compared to published literature. Flow patterns upstream and downstream of the contraction region are analysed at various Reynolds number in the range 44 ≤ R e D ≤ 993 for the large tube and 87 ≤ R e D ≤ 1956 for the small tube, considerating a contraction ratio of β = 1 . 97 . Comparison between numerical and experimental velocity profiles has shown good agreement.

The present paper concerns large-eddy simulations of turbulent downhole flow for six Reynolds numbers and five Taylor numbers. Swirl parameter within the range (0-0.98), which compares the effects of the rotation and the flow rates, was evaluated. In this work, the fluid is injected through the drill pipe and then accelerated by the nozzle. As the fluid discharges from the nozzle, a high speed jet is generated in the downhole region, the fluid then impinges the bottomhole surface and finally flows out the downhole region through the annulus. The nozzle is represented by a sudden contraction. The dynamic subgrid scale model has been used to calculate the turbulent viscosity. The immersed boundary method is employed to represent the solid walls of the proposed geometry. Coherent structures appear as spiral rolls into the nozzle and their inclination angles depend on the rotational speed. When the rotational speed increases, these structures are more aligned with the tangential direction. Due to the geometry of the problem, a toroidal vortex takes place and it grows as the Reynolds number increases. The magnitude of the velocity fluctuations increase in the jet region and near the sidewall with increasing flow rate; it also increased in the jet region with increasing rotational speeds.The impact force and the peak pressure on the impacted surface increases with increasing flow rates. Good agreement of the impact force with other works supports the present work methodology.

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SUMMARYThis study aimed to analyze the geographical distribution of COVID-19 and to identify highrisk areas for the occurrence of cases and deaths from the disease in the indigenous population of Brazil. This is an ecological study whose units of analysis were the Special Indigenous Sanitary Districts. Cases and deaths by COVID-19 notified by the Special Secretariat for Indigenous Health between March and October 2020 were included. To verify the spatial association, the Getis-Ord General G and Getis-Ord Gi * techniques were used. High spatial risk clusters have been identified by the scan statistics technique. 32,041 cases of COVID-19 and 471 deaths were reported. The incidence and mortality rates were between 758.14 and 18530.56 cases and 5.96 and 265.37 deaths per 100 thousand inhabitants, respectively. The non-randomness of cases (z-score = 5.40; p <0.001) and deaths (z-score = 3.83; p <0.001) was confirmed. Hotspots were evidenced for both events with confidence levels of 90, 95 and 99% concentrated in the North and Midwest regions of the country. Eight high-risk spatial clusters for cases with a relative risk (RR) between 1.08 and 4.11 (p <0.05) and two risk clusters for deaths with RR between 3.08 and 3.97 (p <0.05) were identified. The results indicate critical areas in the indigenous territories of Brazil and contribute to better targeting the control actions of COVID-19 in this population.

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