LOCAL PRESSURE CORRECTION FOR THE STOKES SYSTEM

Pressure correction methods constitute the most widely used solvers for the timedependent Navier-Stokes equations.There are several different pressure correction methods,where each time step usually consists in a predictor step for a non-divergence-free velocity,followed by a Poisson problem for the pressure(or pressure update),and a final velocity correction to obtain a divergence-free vector field.In some situations,the equations for the velocities are solved explicitly,so that the numerical most expensive step is the elliptic pressure problem.We here propose to solve this Poisson problem by a domain decomposition method which does not need any communication between the sub-regions.Hence,this system is perfectly adapted for parallel computation.We show under certain assumptions that this new scheme has the same order of convergence as the original pressure correction scheme(with global projection).Numerical examples for the Stokes system show the effectivity of this new pressure correction method.The convergence order O(k^2)for resulting velocity fields can be observed in the norm l^2(0,T;L^2(Ω)).

The influence of pressure waves in tidal gravity records

For the reduction of atmospheric effects,observed gravity has initially been corrected by using the computed barometric admittance k of the in situ measured pressure,expressed in nms-2/hPa units and estimated by least squares method.However,the local pressure changes alone cannot account for the atmospheric mass attraction and loading when the coherent pressure field exceeds a specific size,i.e.,with increasing periodicities.To overcome this difficulty,it is necessary to compute the total atmospheric effect at each station using the global pressure field.However,the direct subtraction of the total gravity effect,provided by the models of pressure correction,is not yet satisfactory for S2 and other tidal components,such as K2 and P1,which include solar heating pressure tides.This paper identifies the origin of the problem and presents strategies to obtain a satisfactory solution.First,we set up a difference vector between the tidal factors of M2 and S2 after correction of the pressure and ocean tides effects.This vector,hereafter denoted as RES,presents the advantage of being practically insensitive to calibration errors.The minimum discrepancy between the tidal parameters of M2 and S2 corresponds to the minimum of the RES vector norm d.Secondly we adopt the hybrid pressure correction method,separating the local and the global pressure contribution of the models and replacing the local contribution by the pressure measured at the station multiplied by an admittance kATM.We tested this procedure on 8 stations from the IGETS superconducting gravimeters network(former GGP network).For stations at an altitude lower than 1000 m,the value of dopt is always smaller than0.0005.The discrepancy between the tidal parameters of the M2 and S2 waves is always lower than0.05% on the amplitude factors and 0.025° on the phases.For these stations,a correlation exists between the altitude and the value kopt.The results at the three Central European stations Conrad,Pecny and Vienna are in excellent agreement(0.05%) with the DDW99NH model for all the main tidal waves.

A Staggered Grid Method for Solving Incompressible Flow on Unstructured Meshes

A finite volume method based unstructured grid is presented to solve the two dimensional viscous and incompressible flow.The method is based on the pressure-correction concept and solved by using a semi-staggered grid technique.The computational procedure can handle cells of arbitrary shapes,although solutions presented in this paper were only involved with triangular and quadrilateral cells.The pressure or pressure-correction value was stored on the vertex of cells.The mass conservation equation was discretized on the dual cells surrounding the vertex of primary cells,while the velocity components and other scale variables were saved on the central of primary cells.Since the semi-staggered arrangement can’t guarantee a strong coupling relationship between pressure and velocity,thus a weak coupling relationship leads to the oscillations for pressure and velocity.In order to eliminate such an oscillation,a special interpolation scheme was used to construct the pressure-correction equation.Computational results of several viscous flow problems show good agreement with the analytical or numerical results in previous literature.This semi-staggered grid method can be applied to arbitrary shape elements,while it has the most efficiency for triangular cells.

A Novel Staggered Semi-implicit Space-Time Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations

A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions.The staggered DG scheme defines the discrete pressure on the primal triangular mesh,while the discrete velocity is defined on a staggered edge-based dual quadrilateral mesh.In this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is proposed.On the primary triangular mesh(the pressure elements),the basis functions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each triangle.On the dual mesh instead(the velocity elements),the basis functions consist in the union of piecewise polynomials of degree N on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries,while they are continuous inside.In other words,the basis functions on the dual mesh arc built by continuous finite elements on the subtriangles.This choice allows the construction of an efficient,quadrature-free and memory saving algorithm.In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations,the arbitrary high order of accuracy in time is achieved through tire use of time-dependent test and basis functions,in combination with simple and efficient Picard iterations.Several numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes,not only from a computer memory point of view,but also concerning the computational time.

Temperature and pressure characteristics of ultrasonic transducer and the amplitude spectra correction of echoes

In this paper,the transfer functions of ultrasonic transducers under different temperatures are imitated according to Mason equivalent circuit. The relevant experiments are carried out. The results show that the transfer characteristic of ultrasonic transducer varies with temperature and pressure. Therefore, we present an approach to correct the amplitude spectra of ultrasonic echoes got in different temperature and pressure environmeots. The theoretical simulation and experimental results prove that the approach is simple, effective and practical.