BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES
Annotation
Stokes flows in cylindrical and spherical geometry are considered. Such flows are rather natural for geophysics. We derive some exact particular solutions of Stokes and continuity equations for particular dependence of viscosity and density on cylindrical coordinates. These solutions correspond to axisymmetric flows for the case when viscosity is a function of radius. We suggest exact particular solutions of Stokes and continuity equations with variable viscosity and density in spherical coordinates for the case of spherically symmetric viscosity and density distributions. We demonstrate how these solutions can be used for creation of test problems suitable for benchmarking numerical algorithms. Examples of such benchmarking are presented. The advantage of this benchmarking approach is the ability to test numerical algorithms for variable viscosity and density gradients. We suggest numerical scheme of multigrid algorithm for solving Stokes and continuity equations with variable viscosity in a spherical coordinate system. Calculations are performed on a sequence of orthogonal staggered grids. The quality of the numerical scheme was verified by comparing the numerical solution with the analytical solution of the test problem.
Keywords
Постоянный URL
Articles in current issue
- TRENDS IN THE DEVELOPMENT OF DETONATION ENGINES FOR HIGH-SPEED AEROSPACE AIRCRAFTS AND THE PROBLEM OF TRIPLE CONFIGURATIONS OF SHOCK WAVES. Part I. Research of detonation engines
- SPECIAL ASPECTS OF INITIAL OPTICAL SCHEME SELECTION FOR DESIGN OF NON-IMAGING OPTICAL SYSTEMS
- APPLICATION OF CHEMOMETRICS FOR ANALYSIS OF BIOAEROSOLS BY FLOW-OPTICAL METHOD
- APPROACH TO AUTOMATION OF LENS COMPONENTS CENTERING FOR ASSEMBLING OF DIFFERENT DESIGN OBJECTIVES
- METHOD FOR CREATION OF SPHERICAL PANORAMAS FROM IMAGES OBTAINED BY OMNIDIRECTIONAL OPTOELECTRONIC SYSTEMS
- LINE-FIELD SWEPT-SOURCE OPTICAL COHERENCE TOMOGRAPHY SYSTEM FOR NEAR INFRARED SPECTRAL REGION
- BACKSTEPPING ALGORITHM FOR LINEAR SISO PLANTS UNDER STRUCTURAL UNCERTAINTIES
- RESEARCH OF FREE MOTION TRAJECTORIES FEATURES OF CONTINUOUS SYSTEM DEFINED AS A CONSECUTIVE CHAIN OF IDENTICAL FIRST-ORDER APERIODIC LINKS
- SPECTRAL CHARACTERISTICS OF MID-INFRARED LIGHT-EMITTING DIODES BASED ON InAs (Sb,P)
- SIMULATION OF SENSING ELEMENT OF TEMPERATURE SENSOR BASED ON SILICATE GLASS WITH SODIUM NANOPARTICLES
- (IN-) PRIVACY IN MOBILE APPS. CUSTOMER OPPORTUNITIES (in Engl.)
- PRINCIPLES OF INDICATION FOR EN-ROUTE FLIGHT PATHS OF THE AIRCRAFT ON THE SCREEN OF ON-BOARD DISPLAY DEVICES
- ERROR CORRECTION METHOD FOR SEQUENCING DATA WITH INSERTIONS AND DELETIONS
- CHOICE OF OPTION FOR IMPLEMENTATION OF THE MULTILEVEL SECURE ACCESS TO THE EXTERNAL NETWORK
- SYNTHESIS OF THE SECONDARY STRUCTURE OF ALGEBRAIC BAYESIAN NETWORKS: AN INCREMENTAL ALGORITHM AND STATISTICAL ESTIMATION OF ITS COMPLEXITY
- EFFECT OF MICROPHONES NON-IDENTITY ON THE MICROPHONE ARRAYS CHARACTERISTICS
- QUALITY CONTROL AUTOMATED LASER-ULTRASONIC METHOD FOR SOLDER JOINTS OF NOZZLES OF CHAMBERS IN LIQUID ROCKET ENGINES
- ROBUST MODIFICATION OF THE LASSO METHOD FOR GENOME-WIDE ASSOCIATION STUDY IN VIEW OF TARGET PHENOTYPE VALUES
- BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES
- INFORMATIONAL MODEL OF MENTAL ROTATION OF FIGURES
- WENO SCHEMES FOR SOLUTION OF UNSTEADY ONE-DIMENSIONAL GAS DYNAMICS TEST PROBLEMS
- AUTOMATED CONTROL SIMULATION OF PROFESSIONAL SKILLS FORMATION FOR PRODUCTION SYSTEM OPERATOR
- STUDY OF OPTICAL AND LUMINESCENT PROPERTIES OF POTASSIUM-ALUMINA-BORATE GLASS DOPED WITH Cr3+ IONS
- SPEAKER-DEPENDENT FEATURES FOR SPONTANEOUS SPEECH RECOGNITION