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Anisotropic Diffusion in SPH Sergei Biriukov Supervisor: Daniel Price <latexit

  1. Anisotropic Diffusion in SPH Sergei Biriukov Supervisor: Daniel Price

  2. <latexit sha1_base64="/40ZQZl38+nSd3lsDdGbpaHusXc=">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</latexit> <latexit sha1_base64="/40ZQZl38+nSd3lsDdGbpaHusXc=">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</latexit> <latexit sha1_base64="/40ZQZl38+nSd3lsDdGbpaHusXc=">ACbHicbVFNb9NAEF2bj5bw5RZxgApRChKD0ROVQTcKiEhjkVKaKU4scabdbPp2rvaHSMiyzd+YW/9C1z4C2xSg0rLSKt982aeduZtZpR0FMcXQXjr9p27G5v3OvcfPHz0ONra/up0ZbkYca20PcnQCSVLMSJSpwYK7DIlDjOzj6u6sfhHVSl0NaGjEp8LSUueRInkqjHwBJbpHXiUFLEtV0H4bN3wzsVMKVZNFAgsZY/R0SVxVp1qo98iI71/6GYc+m2V7vbTJHqm0zlX/At5AMhOKMK0lLJo9+JTWmDVp1I378TrgJhi0oMvaOEqj82SmeVWIkrhC58aD2NCkXo3JlWg6SeWEQX6Gp2LsYmFcJN67VYDu56ZQa6tPyXBmr2qLFwbln4RXYLpLm7XluR/6uNK8rfT2pZmopEyS8fyisFpGFlPcykFZzU0gPkVvpZgc/R20f+gzrehMH1lW+C0X7/Qz/+ctA9fNW6scl2EvWYwP2jh2yz+yIjRhnP4MoeBY8D36FT8Od8MVlaxi0mifsnwhf/wapGrtd</latexit> <latexit sha1_base64="p0hSre0Kf2P5CvIRgh8/t7+wSGM=">ACJ3icbVBNS8NAEN3Ur1q/oh69LFahXkoqgnoQC14ELxVaW2hKmWw37dLNJuxuhBLyc7z4V7yIqOjRf+KmLaitDwYe780wM8+LOFPacT6t3MLi0vJKfrWwtr6xuWVv79ypMJaENkjIQ9nyQFHOBG1opjltRZJC4Ha9IZXmd+8p1KxUNT1KdAPqC+YyANlLXvnR9CSRxI5CaAcf19IfrF9gV4DHwSW9UJfcAPTA85ObdKLi+lHXLjplZw8TypTUkRT1Lr2i9sLSRxQoQkHpdoVJ9KdJFtJOE0LbqxoBGQIfdo2VEBAVScZP5riQ6P0sB9KU0Ljsfp7IoFAqVHgmc7sVDXrZeJ/XjvW/lknYSKNRVksiPTQhzlLDPSYp0XxkCBDJzK2YDMAkp02BRNCZfbledI4Lp+XnduTYvVgmkYe7aF9VEIVdIq6BrVUAMR9ICe0Ct6sx6tZ+vd+pi05qzpzC76A+vrG53DpmU=</latexit> <latexit sha1_base64="p0hSre0Kf2P5CvIRgh8/t7+wSGM=">ACJ3icbVBNS8NAEN3Ur1q/oh69LFahXkoqgnoQC14ELxVaW2hKmWw37dLNJuxuhBLyc7z4V7yIqOjRf+KmLaitDwYe780wM8+LOFPacT6t3MLi0vJKfrWwtr6xuWVv79ypMJaENkjIQ9nyQFHOBG1opjltRZJC4Ha9IZXmd+8p1KxUNT1KdAPqC+YyANlLXvnR9CSRxI5CaAcf19IfrF9gV4DHwSW9UJfcAPTA85ObdKLi+lHXLjplZw8TypTUkRT1Lr2i9sLSRxQoQkHpdoVJ9KdJFtJOE0LbqxoBGQIfdo2VEBAVScZP5riQ6P0sB9KU0Ljsfp7IoFAqVHgmc7sVDXrZeJ/XjvW/lknYSKNRVksiPTQhzlLDPSYp0XxkCBDJzK2YDMAkp02BRNCZfbledI4Lp+XnduTYvVgmkYe7aF9VEIVdIq6BrVUAMR9ICe0Ct6sx6tZ+vd+pi05qzpzC76A+vrG53DpmU=</latexit> <latexit sha1_base64="p0hSre0Kf2P5CvIRgh8/t7+wSGM=">ACJ3icbVBNS8NAEN3Ur1q/oh69LFahXkoqgnoQC14ELxVaW2hKmWw37dLNJuxuhBLyc7z4V7yIqOjRf+KmLaitDwYe780wM8+LOFPacT6t3MLi0vJKfrWwtr6xuWVv79ypMJaENkjIQ9nyQFHOBG1opjltRZJC4Ha9IZXmd+8p1KxUNT1KdAPqC+YyANlLXvnR9CSRxI5CaAcf19IfrF9gV4DHwSW9UJfcAPTA85ObdKLi+lHXLjplZw8TypTUkRT1Lr2i9sLSRxQoQkHpdoVJ9KdJFtJOE0LbqxoBGQIfdo2VEBAVScZP5riQ6P0sB9KU0Ljsfp7IoFAqVHgmc7sVDXrZeJ/XjvW/lknYSKNRVksiPTQhzlLDPSYp0XxkCBDJzK2YDMAkp02BRNCZfbledI4Lp+XnduTYvVgmkYe7aF9VEIVdIq6BrVUAMR9ICe0Ct6sx6tZ+vd+pi05qzpzC76A+vrG53DpmU=</latexit> Diffusion in SPH ∂ T ∂ 2 T m b X r i ˆ r j − δ ij ) F ab ∂ t = r · ( K r T ) T ( r b )(5ˆ ∂ r i ∂ r j ≈ ρ b b Heat Conduction Radiative Transfer Gas-Dust Fraction

  3. Initial Isotropic Anisotropic ' ( ' ( ! = # ∗ 1 0 ! = 1 0 ' ' 0 1 0 0 ( (

  4. Question Isotropic Anisotropic

  5. Smoothing Length !"#$%&'() *+(# $ℎ( )ℎ"-( *. / 0 − )-'%2( .*# 3%..(#(2$ )4**$ℎ%25 '(25$ℎ . | – # 78 have only X – # 78 have two – all of the one non-zero non-zero # 78 components are component component not zero

  6. Good Outer Part – Good Kernel 1" Outer part more important! 2" Shapes are Shapes are Shapes are different… different. different. 3" …but errors are the same. %&'()* *&+,-./,-& 0ℎ.2&0 (3 4&+)&5 36)'/,()0. 8++(+ /&+90 3(+ :.25.',.) (2&+./(+.

  7. Understanding Brookshaw Method Brookshaw method a W = � 2( r · r W ) � 2 f 0 ( q ) r 2 = + ( r · r ) C ν h ν +2 q With Gaussian = The kernel itself is a − 2 q exp ( − q 2 ) exp ( − q 2 ) − 2 = 4 = 4 W f 2 nd derivative C ν h ν +2 h 2 h 2 q C ν h ν

  8. Isotropic Diffusion Operators 1" 2" 3" %&'()*+,&- &. / 0 − 2**&* 3+4ℎ *26)*7, 4& -8'92* &. -2+6ℎ9&*, . Cubic spline as kernel function. All dimensions.

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